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# Sound System Specification

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## Oli Brand

on 27 April 2016

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#### Transcript of Sound System Specification

CORC2079
Sound System Specification
& Operation

Acoustics Recap
Fundamentals of sound
Particle Motion
Propagation of Sound
Speed of Sound
Wavelength and Frequency
Harmonics
Particle Motion
Air particles could be compared to the hairs on your head. As the air blows your hair it moves back and forth with the breeze but stay routed

This movement is closely related to how the air molecules move when disturbed

They move a short distance (a few ten thousandths of an inch) but stay confined to their allocated area

Note maximum velocity
Propagation of Sound
One cubic inch of air contains more than a million air molecules

As the speaker driver pushes out it squashes the air molecules together making them compress. The area of compressed air molecules then has a greater pressure than it did before it was squashed

The area around the compressed air now has fewer molecules and and such has a pressure less than before. Therefore sound is a mechanical wave and requires a medium to travel through
Speed of Sound
The speed at which sound propagates (or travels from its source) is directly influenced by both the medium through which it travels and the factors affecting the medium, such as altitude, humidity and temperature for gases like air

To calculate the speed of sound in dry air at sea level, use the following formula:

V = 331.4 + 0.6Tc

V = velocity (m/s), Tc = temperature in Celsius
If the temperature is 20 degrees C what is the speed of sound:
V = 331.4 + 0.6Tc
V = velocity (m/s),
Tc = temperature in Celsius

V = 331.4 + (0.6x20)
V = 331.4 +12
V = 343.4
It’s useful to know this speed in different units for making acoustic measurements:
343 meters per second
1126 feet per second
768 miles per hour

The speed of light is 670,616,629 miles per hour
The faintest sound the ear can hear (20 μPa) exists at a pressure some 5,000 million times smaller than atmospheric pressure.
Phase
Partials
Octaves
Spectrum
Electrical, Mechanical and Acoustical Analogues
Particles involved in the propagation of sound waves can move with
(A) circular motion, (B) transverse motion, or (C) longitudinal motion
Newton's and Pascal's
The Pascal (Pa) is a measurement of force per unit area, defined as one Newton per square meter
One Newton is the amount of force it takes to accelerate a 1 kilogram object by one meter per second (m/s)
The benchmark threshold of hearing, in other words the smallest perceptible amplitude, is approximately 20µPa
A micro (µ) Pascal is 1 millionth of a Pascal
1 Pa = 1N/m^2
1 µPa = 0.000001 N/m^2
20 µPa = 0.00002 N/m^2
Measurements
Air pressure is measured in Bars and 1 Bar = 10^5 Pascals
or 10,000 Pascals

About 4,900 ft/sec in freshwater and
around 16,700 ft/sec in steel
Various mediums
Sounds travels a different speeds depending on the medium

Do you think it travels faster or slower in water and why?
Wavelength and Frequency
A sinusoidal wave has an easily measured wavelength - that is between two corresponding points of the wave
The amount of cycles per second is measured in Hertz
Wavelength = speed of sound / frequency
Wavelengths
What are the wavelengths (in feet) of the following frequencies:
A. 20 Hz
B. 74 Hz
C. 500 Hz
D. 1kHz
E. 5kHz
F. 20kHz
It is vital to understand that the higher the frequency the shorter the wavelength
Harmonics
Frequencies
Bats in the UK use frequencies well above our own perception

The Common Pipistrelle uses an Echolocation frequency of 39kHz
The Lesser Horseshoe 108kHz

Much higher frequencies, in the range 1-20 MHz, are used for medical ultrasound
It is not very often that will deal with simple waves such as the sine wave but use complex waves such as speech and music in audio reproduction

Any complex periodic wave can be recreated using sine waves at different frequencies, amplitude and phase

This was proven to be true by a French Mathematician called Joseph Fourier
Harmonics
f2 = 2f1
f3 = 3f1
Harmonics
The sine wave with the lowest frequency ( f1) is called the fundamental

The sine wave that is twice the frequency ( f2) is called the second harmonic, and the sine wave that is three times the frequency ( f3) is the third harmonic, and so on.
Phase
The time relationship between the fundamental and the harmonic series is not always exact. The harmonics of a sound differ in their start time and alter the phase relationship of these harmonics
Driver Phase
3-Phase Power
Sound Systems
Transmission Levels
Transmit
Verb
Cause (something) to pass on from one place or person to another
Broadcast or send out (an electrical signal or a radio or television program)
Transmission Goal
When relaying audio signal between devices we assess the accuracy of transmission by how closely the final signal traces the original

The path of transmission moves from acoustical energy to electrical and then back to the original acoustic form

Throughout this process our goal is to minimize distortion and get as close to that original form as possible

This is in fact, a near impossibility and we can hope to make as many informed judgements of sound quality as we can to correct and realign any disturbances to the waveform

Line Level Electronic - Speaker Level Electronic - Acoustic
Transmission
Amplitude / Magnitude
Cycle
Period
Frequency
Phase
Medium
Transduction
Wavelength
Pressurisation / Compression
Rarefaction
Voltage
AC / DC
Explain the following terms:
Transmission
Amplitude - electrons or molecules moving forwards and backwards in constant motion. The extent of this change is called Amplitude and sometimes referred to as Magnitude
Cycle - One movement of molecules or electrons, forward and backwards from the origin, is a cycle
Period - One round trip of this forward and backwards motion is measured in time (m/s) and called a Period
Frequency - The number of these cycles per second is referred to as the Frequency measured in Hertz (Hz). This starts and ends at the same place anywhere within the radius of cycle
Transmission
Phase - In order to know where in the circle we are starting we measure, in degrees, the Phase of the wave
0° being the origin of the wave 180° being halfway through the cycle
Transmission
Medium - For transmission to take place of an audio signal needs a medium to travel through made from molecules or electrons
Transduction - For the audio signal to pass from one media to another there must be a transfer of energy called transduction
Wavelength - The distance the audio signal moves within the medium to complete one cycle forward and backwards. The size of the wavelength for a given frequency is proportional to the transmission speed of our medium.
Slight difference in Phase
Using two signal, say 440Hz and 441Hz, it is possible to hear the positive and negative effect of the phase between the 2 signals
Mismatch of driver alignment can result in negative phase within the output of a single loudspeaker - this can also be an issues with acoustic crossovers within the system
Transmission
Pressurisation / Compression - The sound wave energy forces air molecules together creating a higher air pressure - the positive part of the wave
Rarefaction - On the other half of the cycle we have a low pressure. Less than the natural ambient pressure of 1 bar
Voltage - The electrical equivalent of this pressure is voltage
AC/DC - The positive and negative air pressure is represented by positive and negative voltage pushing backwards and forwards creating an Alternating Current as it operates above and below the ambient voltage know as Direct Current
Waveform
The waveform can exist in a simple form, such as a sine wave, but this isn't often and we are mainly dealing with very complex waves made up of multiple frequencies summed into one overarching waveform
Waveform
The higher frequency is added to the lower frequency and in the case of the final waveform all 3 frequencies are visible
Waveform
3 visual forms of an audio signal
Transmission Levels
When quantifying transmission we use decibels which provides a handy why of comparing the ratio of very large values
To make sense of this we must have a relative value to compare the ratio with. This can be an industry standard or a comparison between to signals - regardless of value
When comparing the input value of a device to the output value, the ratio of these two signals is know as the gain of the device
Levels
Levels
Ratios versus differences
Using logs is convenient way of calculating these ratios as its logarithmic nature is similar to the way our ear perceive sound

Human hearing is highly nonlinear: in order to double the perceived intensity of a sound, the actual sound power must be multiplied by a factor of ten
Both the chemical Ph scale and the Richter scale work logarithmically
The formula for calculating the difference in dB of the ration of input to output power of a device is as follows:
1. Power into an amplifier is 1 Watt, the power out is 10 Watts. Find the power gain in dB
2. Power into an amplifier is 1 Watt, the power out is 40 Watts. Find the power gain in dB.
Large concerts and productions need a power supply that can deliver and greater potential and more consistent supply
Partials
Harmonics are, as we know, an integer of the fundamental frequency. Partials are the name given to non-integer harmonics yet richness of tone can still be imparted by such deviations from the true harmonic relationship
What instruments demonstrate a strong non-integer relationship within the harmonics of their sound?
Spectrum
Octaves
The octave is a logarithmic concept that is firmly embedded in musical scales and terminology because of its relationship to the ear’s characteristics
Harmonics are linearly related and octaves are logarithmic
Write down the first 5 harmonic series of a square wave with a fundamental of 43.65Hz (F1)
Write down the frequencies for the next 4 octaves starting 43.65Hz (F1)
Octave
We can use a formula to calculate frequencies bands based around the octave's logarithmic nature
f2 = upper edge of band
f1 = lower edge of band
n = number of octaves
Octave
The low-frequency limit of a band is 20 Hz, what is the high-frequency limit of a band that is 10 octaves wide?
If 446 Hz is the lower limit of a 1/3-octave band, what is the frequency of the upper limit?
What is the frequency of the lower limit of an octave band centered on 2,500 Hz?
What is the upper limit?
What is the lower limit of a 1/3-octave band centered on 1,000 Hz? The f1 is 1,000 Hz but the lower limit would be 1/6-octave lower than the 1/3-octave, so n = 1/6
f2/20 Hz = 2^10
f2 =(20)(2^10)
f2 =(20)(1,024)
f2 = 20,480 Hz
f2/446=(2^1/3)
f2 =(446)(2^1/3)
f2 = (446)(1.2599) f2 = 561.9 Hz
f2/f1 = 1000/f1 = 2^1/6
f = 1,000/2^1/6
f1= 1,000/1.12246
f1 = 890.9 Hz
2500/f1 = 2^1/2
f1 = 2500/2^1/2
f1 = 2500/1.4142
f1 = 1767.8 Hz
f2/25000 = (2^1/2)
f2 = (2500)/(2^1/2)
f2 = (2500)/(1.4142)
f2 = 3535.5 Hz
Light has a spectrum some of which we can see there is light outside of our visible spectrum including far-ultraviolet light because the frequency of its electromagnetic energy is too high for the eye to perceive and far-infrared light because its frequency is too low
Spectrum
Complex waveforms are made from many multiple sine waves combined and varying frequency, amplitude and phase
Our ears has a range of roughly 20Hz to 20kHz
There are frequencies below (infrasound) and above (ultrasound) that we cannot perceive as sound
Electrical, Mechanical, and Acoustical Analogs
Inductance in an electrical circuit is equivalent to mass in a mechanical system and inertance in an acoustical system. Capacitance in an electrical circuit is analogous to compliance in a mechanical system and capacitance in an acoustical system. Resistance is resistance in all three systems, whether it is the fric- tional losses offered to air-particle movement in glass fiber, frictional losses in a wheel bearing, or resistance to the flow of current in an electrical circuit.
"Imagine a sound source set up in a room completely protected from interfering noise. The sound source is adjusted for a weak sound with a sound pressure of 1 unit, and its loudness is carefully noted

In observation A, when the sound pressure is increased until it sounds twice as loud, the level dial reads 10 units. For observation B, the source pressure is increased to 10,000 units. To double the loudness, we find that the sound pressure must be increased from 10,000 to 100,000 units. The results of this experiment can be summarized as follows:"
Ratios versus differences
"Observations A and B accomplish the same doubling of perceived loudness. In observation A, this was accomplished by an increase in sound pressure of only 9 units, where in observation B it took 90,000 units.

Ratios of pressures seem to describe loudness changes better than differences in pressure. Ernst Weber, Gustaf Fechner, Hermann von Helmholtz, and other early researchers pointed out the importance of using ratios in such measurements.

Ratios apply equally well to sensations of vision, hearing, vibration, or even electric shock. Ratios of stimuli come closer to matching human perception than do differences of stimuli. This matching is not perfect, but close enough to make a strong case for expressing levels in decibels."

Everest, F. 2001. The master handbook of acoustics.
New York: McGraw-Hill.
Sound Levels
References/Images
Everest, F. 2001. The master handbook of acoustics. New York: McGraw-Hill.
Mccarthy, B. 2007. Sound systems. Oxford: Focal.
Platt, C. 2009. Make: electronics. Sebastopol, Calif.: O'Reilly.
Acoustic Levitation
Using exponential form we can simplify very large numbers to make them more manageable
Write down the exponential of the following:
1,000,000 = 10 x 10 x 10 x 10 x 10 x 10 = ?
100 = 10 x 10 = ?
10,000 = 10 x 10 x 10 x 10 = ?
0.001 = 1/(10 x 10 x 10) = ?
0.1= 1/10 = ?
0.00001 = 1/(10 x 10 x 10 x 10 x 10) = ?

10^6
10^2
10^4
10^13
10^-1
10^-5
Levels
As we have already discussed, the threshold of hearing can be described in Pascals (1 Pascal is equal to 1newton per meter squared) - remember: 20µPa (0.00002 N/m^2)
But it can also be described in Watts per meter squared (Acoustic intensity is acoustic power per unit area in a specified direction)
So the threshold of hearing is also about 10^-12W/m^2 and a sound at the upper limit would be 10W/m^2
Write 10^-12 as a decimal number
Levels
The range of intensity from the softest sound to a painfully loud sound is 10,000,000,000,000 - demonstrate how we get this result
Write this number down as an exponential
10^-12 W/m2 has been establish as the reference for intensity - remember decibels are a ration between to numbers
To calculate sound intensity ratio divide the intensity by the intensity reference 10^-12 W/m2
What is the sound intensity of 10^-9 W/m2?
Levels
So far we have been able to represent large decimal numbers by their exponential equivalent

10 x 10 x 10 = 10^3 = 1000

Here we find that logarithms are extremely useful as they are calculated proportionally

log10(100) = 2
Here we define the following as 'the logarithm of 100 to the base 10 equals 2'
Levels
In its simplest form, a logarithm answers the question:
log10(1000) = 3
How many of one number do we multiply to get another number?
In this example: the number of 10 you need to multiple to get 1000
base
logarithm
What is: log5(625)?
In other words, how many 5s need to be multiplied together to get 625?

Electronics
Experimenting with Electricity
Multimeter
A multimeter is a devise used to measure voltage, resistance and current in electronics & electrical equipment

It is also used to test continuity between to 2 points to verify if there is any breaks in circuit or line
Multimeter
On a manual-ranging meter, you select the range, and if the source that you are measuring is outside of that range, the meter tells you that you made an error.

The trouble is that this can trick you into making errors. What if the battery is almost dead? Then you may be measuring a fraction of a volt without realizing it.
Multimeter
Moisten your tongue and touch the tip of it to the metal terminals of a 9-volt battery. The sudden sharp tingle that you feel is caused by electricity flowing from one terminal of the battery, through the moisture on and in your tongue, to the other terminal.

Because the skin of your tongue is very thin (it’s actually a mucus membrane) and the nerves are close to the surface, you can feel the electricity very easily.

Now stick out your tongue, dry the tip of it very thoroughly with a tissue, and repeat the experiment without allowing your tongue to become moist again. You should feel less of a tingle.

What’s happening here? We’re going to need a meter to find out.
There are two types of multimeter Analog & Digital
Analog has a needle style gauge
Digital has a LCD display (PPT)
Multimeter
Most meters have removable wires, known as leads. Most meters also have three sockets on the front, the leftmost one usually being reserved to measure high electrical currents (flows of electricity). We can ignore that one for now.

The leads will probably be black and red. The black wire plugs into a socket labeled “COM” or “Common.” Plug the red one into the socket labeled “V” or “volts.”
Multimeter
The other ends of the leads terminate in metal spikes known as probes, which you will be touching to components when you want to make electrical measurements.

The probes detect electricity; they don’t emit it in significant quantities. Therefore, they cannot hurt you unless you poke yourself with their sharp ends.

If your meter doesn’t do autoranging, each position on the dial will have a number beside it. This number means “no higher than.”

For instance if you want to check a 6-volt battery, and one position on the voltage section of the dial is numbered 2 and the next position is numbered 20, position 2 means “no higher than 2 volts.” You have to go to the next position, which means “no higher than 20 volts.”
Ohms & Resistance
Resistance
We’re going to use the meter to discover the electrical resistance of your tongue. First, set your meter to measure resistance. If you have to set the range manually, begin with no less than 100,000 ohms (100K).

Touch the probes to your tongue, about an inch apart. Note the reading, which should be around 50K.

Now put aside the probes, stick out your tongue, and use a tissue to dry it very carefully and thoroughly. Without allowing your tongue to become moist again, repeat the test, and the reading should be higher.

Finally, press the probes against the skin of your hand or arm: you may get no reading at all, until you moisten your skin.

Can you think of an example where skin moisture is used to take a reading for analysis?
Resistance
A 9-volt battery contains chemicals that liberate electrons (particles of electricity), which want to flow from one terminal to the other as a result of a chemical reaction inside it.

Think of the cells inside a battery as being like two water tanks - one of them full, the other empty. If they are connected with a pipe, water flows between them until their levels are equal.

Similarly, when you open up an electrical pathway between the two sides of a battery, electrons flow between them, even if the pathway consists only of the moisture on your tongue
Resistance
Resistance
Attach the snap-on terminal cap to the 9-volt battery. Take the two wires that are attached to the cap and hold them so that the bare ends are just a few millimeters apart. Touch them to your tongue. Now separate the ends of the wires by a couple of inches, and touch them to your tongue again. Notice any difference?

Use your meter to measure the electrical resistance of your tongue, this time varying the distance between the two probes. When electricity travels through a shorter distance, it encounters less total resistance. As a result, the current (the flow of electricity per second) increases. You can try a similar experiment on your arm.

Use your meter to test the electrical resistance of water. Dissolve some salt in the water, and test it again. The world around you is full of materials that conduct electricity with varying amounts of resistance.

Measure the resistance of different materials in the studio
Electrical Abuse
To get a better feeling for electrical power, you’re going to do what you're told not to do. You’re going to short out a battery. A short circuit is a direct connection between the two sides of a power source.
Short Circuits

Short circuits can be dangerous. Do not short out a power outlet in your home: there’ll be a loud bang, a bright flash, and the wire or tool that you use will be partially melted, while flying particles of melted metal can burn you or blind you.

If you short out a car battery, the flow of current is so huge that the battery might even explode, drenching you in acid.

Lithium batteries are also dangerous. Never short-circuit a lithium battery: it can catch fire and burn you.

Use only an alkaline battery in this experiment, and only a single AA cell. You should also wear safety glasses in case you happen to have a defective battery.
Short circuit
Use an alkaline battery. Do not use any kind of rechargeable battery.
Put the battery into a battery holder that’s designed for a single battery and has two thin insulated wires emerging from it. Do not use any other kind of battery holder.

Use an alligator clip to connect the bare ends of the wires. There will be no spark, because you are using only 1.5 volts. Wait one minute, and you’ll find that the wires are getting hot. Wait another minute, and the battery, too, will be hot.
The low internal resistance of lithium batteries (which are often used in laptop computers) allows high currents to flow, with unexpected results.

Never fool around with lithium batteries
Voltage
The heat is caused by electricity flowing through the wires and through the electrolyte (the conductive fluid) inside the battery. If you’ve ever used a hand pump to force air into a bicycle tire, you know that the pump gets warm.

Electricity behaves in much the same way. You can imagine the electricity being composed of particles (electrons) that make the wire hot as they push through it. This isn’t a perfect analogy, but it’s close enough for our purposes.

Chemical reactions inside the battery create electrical pressure. The correct name for this pressure is voltage, which is measured in volts and is named after Alessandro Volta, an electrical pioneer.
Voltage
Going back to the water analogy: the height of the water in a tank is proportionate to the pressure of the water, and comparable to voltage.

But volts are only half of the story. When electrons flow through a wire, the flow is known as amperage, named after yet another electrical pioneer, André- Marie Ampère.

The flow is also generally known as current. It’s the current - the amperage - that generates the heat.
Voltage
Why didn’t your tongue get hot?

When you touched the 9-volt battery to your tongue, you felt a tingle, but no perceptible heat. When you shorted out a battery, you generated a noticeable amount of heat, even though you used a lower voltage. How can we explain this?

The electrical resistance of your tongue is very high, which reduces the flow of electrons. The resistance of a wire is very low, so if there’s only a wire connecting the two terminals of the battery, more current will pass through it, creating more heat. If all other factors remain constant:
• Lower resistance allows more current to flow
• The heat generated by electricity is proportional to the amount of electricity (the current) that flows.

Here are some other basic concepts:
• The flow of electricity per second is measured in amperes, or amps.
• The pressure of electricity causes the flow, measured in volts.
• The resistance to the flow is measured in ohms.
• A higher resistance restricts the current.
• A higher voltage overcomes resistance and increases the current.
Voltage
V = IR

Re-arrange this formula to find I then R
If a circuit has a pressure of 12 Volts and a resistance of 6 Ohms what is the current?

If a circuit has a pressure of 12 volts and a resistance of 1 Ohms what is the current?

If a circuit has a pressure of 12 volts and a resistance of 12 Ohms what is the current?
Fuses
If you’re wondering exactly how much current flows between the terminals of a battery when you short it out, that’s a difficult question to answer. If you try to use your multimeter to measure it, you’re liable to blow the fuse inside the meter. Still, you can use your very own 3-amp fuse, which we can sacrifice because it didn’t cost very much.

First inspect the fuse very carefully. You should see a tiny S-shape in the transparent window at the center of the fuse. That S is a thin section of metal that melts easily.

Remove the battery that you short-circuited. It is no longer useful for anything. Put a fresh battery into the battery carrier, connect the fuse, and take another look. You should see a break in the center of the S shape, where the metal melted almost instantly. This is how a fuse works: it melts to protect the rest of the circuit. That tiny break inside the fuse stops any more current from flowing.
Electricity:
a form of energy resulting from the existence of charged particles (such as electrons or protons), either statically as an accumulation of charge or dynamically as a current
Electricity travels at 186,000 miles per second, that's 7.5 times round the earth in 1 second
Electronics:
the science dealing with the development and application of devices and systems involving the flow of electrons in a vacuum, in gaseous media, and in semiconductors.
Types of Electricity
Static electricity

Objects can be positively charged, negatively charged or neutral (no charge).

A substance that gains electrons becomes negatively charged, while a substance that loses electrons becomes positively charged.

When a charged object comes near to another object they will either attract or repel each other.

If the charges are the same - they repel
If the charges are opposite - they attract
If one is charged and the other is not - they attract
This type of static electricity can be formed by moving across carpet an rubbing balloons
Types of Electricity
Dynamic electricity

Movement of electric charge in a conductor, vacuum, gaseous medium or semiconductor

Lighting starts with a build of static charge between the earth and the sky - when the lighting strikes we have dynamic charge moving between the two.
Electricity
Electric current is the flow of electric charge. Some insulating materials become electrically charged when they are rubbed together.

A substance that gains electrons becomes negatively charged, while a substance that loses electrons becomes positively charged.

The upper wire has no potential difference across it. The electrons are randomly moving in all directions with no flow in one particular direction. Therefore this wire is not carrying any current. The lower wire has a potential difference across A and B. It makes the electrons flow in a particular direction and therefore this wire is carrying a current.
Types of Material
Conductors (metals) - conduct electricity - low resistance

Insulators (rubber, plastic) - don't conduct electricity easily - high resistance

Semiconductors (Silicon, Germanium) - conduct electricity under certain conditions
Fundamentals
How many millivolts or milliamps are the following?:
0.005 volts
0.025 volts
2 volts
0.45 amps
0.152 amps
0.032 amps
Circuits
You will need:

• 1.5-volt AA batteries. Quantity: 4.
• Four-battery holder. Quantity: 1.
• Resistors: 470Ω, 1K, and either 2K or 2.2K (the 2.2K value happens to be more common than 2K, but either will do in this experiment). Quantity: 1 of each resistor.
• An LED, any type. Quantity: 1.
• Alligator clips. Quantity: 3.

From the resistors provided use the multimeter to find the 3 correct value resistors needed for this circuit
Amps
Born in 1775 in France, André- Marie Ampère was a mathematical prodigy who became a science teacher, despite being largely self-educated in his father’s library.

His best-known work was to derive a theory of electromagnetism in 1820, describing the way that an electric current generates a magnetic field. He also built the first instrument to measure the flow of electricity (now known as a galvanometer), and discovered the element fluorine.
Resistors
Resistors
LED
LEDs are much smarter than lightbulbs: they convert almost all their power into light (not light and heat), and they last almost indefinitely—as long as you treat them right
An LED is quite fussy about the amount of power it gets, and the way it gets it. Always follow these rules:
• The longer wire protruding from the LED must receive a more positive volt- age than the shorter wire.
• The voltage difference between the long wire and the short wire must not exceed the limit stated by the manufacturer.
• The current passing through the LED must not exceed the limit stated by the manufacturer.
Circuit
To complete a circuit we will need a source and a load

The source in this case is the battery (where the electricity comes from)

The load in this case is the resistor and the LED (where the electricity is used)
To ensure all the batteries are working test them with the multimeter. You should get a reading of around 1.5 volts each making 6 volts overall
Circuit
To start with use the 2.2KΩ resistor and then swap for the 1K and then the 470K. Observe what happens to the LED
Levels
There are two types of log formulas applicable in audio:
There are two types of log formulas applicable in audio:Power-related equations use the 10 log version, while pressure (SPL) and voltage related equations use the 20 log version. It is important that the proper formula be used since a doubling of voltage is a change of 6 dB while a doubling of power is a change of 3dB.
Capacitors
A capacitor is a discrete component that can store an electrical charge. The larger the capacitance the more charge it can store.
The unit of measurement of capacitance is the farad. Often you will see capacitors of much less than a farad. These will be measured in microfarads (one millionth of a farad or 1/1,000,000) or picofarads (one million-millionth of a farad or 1/1,000,000,000,000).
There are two types of capacitor:
polarised or electrolytic capacitors
non-polarised or non-electrolytic capacitors
Electrolytic capacitors
Polarised or Electrolytic capacitors:

These generally have larger capacitance values. Polarised capacitors have a positive pole and a negative pole, so they must be connected to a circuit the correct way round.

Mounting of polarised capacitors
Polarised capacitors may be either axially mounted (on their side, connected at each end) or radially mounted (upright with both connections at the bottom).
Electrolytic capacitors
Non-polarised or non-electrolytic capacitors:

These are usually much smaller than the polarised type, and have smaller capacitance values. These might range from a few picofarads to a few microfarads. They don't have positive or negative poles so they can be connected to a circuit either way round.
Applications of capacitors

Capacitors are used to smooth rectified alternating-current voltages into steady direct-current voltages. They can also be used to filter out fluctuations in a signal.

Capacitors are often used in series with resistors to achieve a time delay. The time it takes for the capacitor to become charged is related to the size of the capacitor and the value of the regulating resistor.
Sound Levels
The decibel scale is preferred by operators over the linear scale for its relative ease of expression. Expressed linearly we would find ourselves referring to the signal in microvolts, millivolts and volts with various sets of number values and ranges. Such scaling makes it difficult to track a variable signal such as music.
If we wanted to double the signal level we would have to first know the voltage of the original signal and then compute its doubling. With dynamically changing signals such as music, the level at any moment is in flux, making such calculations impractical. The decibel scale provides a relative change value independent of the absolute value.
Hence: 6dB = a doubling, regardless
Levels
dBV and dBu are the most common currently. These are referenced to different values of 1.0 volt and 0.775 volt respectively.
http://www.sengpielaudio.com/calculator-amplification.htm
The difference between these is a fixed amount of 2.21 dB.
Levels
dBV and dBu are the most common currently. These are referenced to different values of 1.0 volt and 0.775 volt respectively.
Audio Cables
Interconnection
True craftsmanship requires a thorough understanding of the materials you’re working with, an understanding that can be gained only through experience.
Introduction
Components of a wire
(1) Copper strands.
(2) Conductor (strands + jacket)
(3) Shield – in this case a metalized mylar foil
(4) Wire.
Wire
Strands are the individual copper strands of a wire.

Conductors are made up of copper strands that are covered with an insulating jacket (different colors of pliable plastic).

Shield is a metallic, conductive layer wrapped around the inner conductors to reduce noise. It may be a metalized mylar foil, an electrically conductive plastic or actual strands of copper wire that are commonly not insulated.

Wires are made up of the conductors (strands and insulating jackets) in a shield, and commonly surrounded by an outer plastic or rubber jacket.

The copper strands go into an insulating jacket to become conductors. Conductors and their shields in an outer jacket are wires. Wires are bundled together to become harnesses or cables
Shield
In spiral shield wire the shield layer is actual strands of copper, wound in a spiral around the inner conductors.

The two inner conductors here are the blue and the translucent-over-copper colored items in the picture.

The two thinner pale white strands have no electrical function, they are ‘packing strands’ that help keep the wire round when it’s made.

This type of wire is stronger and more noise-resistant then the mylar shield type but it’s also larger and costs more. It’s flexible and fast to work with, as opposed to the braided shield wire
Shield
Braided shield wire offers top notch shielding, and it’s very durable.

But it’s a real pain to work with, because you have to carefully unbraid the shield to connectorize it. Not recommended for the impatient.

The three types of wire all do the same thing, but they look different, require different techniques, and offer different pros and cons in terms of use.
Stripping Wire
No matter what type of wire you’re working with, the goal is always the same: to strip off the outer insulating jacket without harming the delicate insulation of the inner conductors.
Wire strippers can be used to remove a short length of the outer jacket. This is best done by adjusting the depth-of-cut on the wire strippers to go almost through the outer jacket. Then grasp the wire with the jaws of the strippers at the cutaway point, clamp down the jaws on the wire and use a rotating, rocking motion to chew most of the way through the outer insulation jacket.
Stripping Wire
Press the wire down onto the exposed edge of the razor blade and carefully roll it back and forth. Keep the downward pressure constant and keep your fingers away from the edge of the blade.

Also, keep the wire exactly at a 90-degree angle to the edge of the blade, so as to avoid making a spiraling cut. This will (if properly done) create a perfectly smooth and accurate cut in the outer jacket – far cleaner than is possible with any other method.

Power
Electrical energy is a combination of two measurable quantities: voltage and current. The electrical power in a DC circuit is expressed as:
P = VI
The power is the product of these two factors. 100 watts of electrical power could be the result of 100 volts at 1 ampere, 10 volts at 10 amperes, 1 volt at 100 amperes, etc. The power could be used to run a single heater at 100 watts, or 100 heaters at 1 watt each.
Levels
These DC formulas are applicable to the purely resistive components of the current-limiting forces in the electrical circuit. In the case of our audio waveform, which is by definition an AC signal, the measure of resistive force differs over frequency.
This complex term for resistance with a frequency component is impedance. The impedance of a circuit at a given frequency is the combination of the DC resistance, and the reactance.
Levels
The reactance is the value for variable resistance over frequency and comes in two forms: capacitive and inductive.

The impedance for a given circuit is a combination of the three resistive values: DC resistance, capacitive reactance and inductive reactance.

These factors alter the frequency response in all AC circuits; the question is only a matter of degree of effect.
Sound Systems
Loudspeaker Specifications
Frequency & Phase Response
A device with no differences over frequency, also known as a "flat" frequency response, is actually the absence of a frequency response.

In our practical world this is impossible, since all audio devices, even oxygen-free hypoallergenic speaker cable, change their response over frequency. The question is the extent of detectible change within the frequency and dynamic range of our hearing system.
Amplitude vs Frequency
Amplitude vs. frequency is a measure of the level deviation over frequency.

The frequency range is generally given as the -3 dB points in electronic devices, while -6 and -10 dB figures are most often used for speakers. The quality of the amplitude response is determined by its degree of variance over the transmission range, with minimum variance corresponding to the maximum quality.
Phase vs Frequency
Phase vs. frequency is a measure of the time deviation over frequency (phase response). A device is specified as having a degree of variation within the operational range governed by the amplitude response. The quality of the phase response is determined by its degree of variance over the transmission range, with minimum variance again corresponding to the maximum quality.

Phase response always merits a second-place finish in importance to amplitude response for the following reason: if the amplitude value is zero there is no level, and the phase response is rendered academic. In all other cases, however, the response of phase over frequency will need to be known.
Phase Response
Let's apply this principal to a musical event: a piano key is struck and the transient pressure peak contains a huge range of frequency components, arranged in the distinct order that our ear recognizes as a piano note. To selectively delay some of the portions of that transient peak rearranges the sequences into a waveform that is very definitely not the original and is less recognizable as a piano note. As more phase shift is added, the transient becomes increasingly stretched over time. The sense of impact from a hammer striking a string will be lost.
Phase
If two speakers are a foot apart, how much phase shift will occur?
What will be the effect on the frequency response of reflections from a wall? These are the kinds of questions we can answer if we have a practical grasp of phase

Because phase describes the relative time difference between two signals, it can be expressed in degrees or radians, which measure the completed portion of a circular period or wavelength.

For example, 90° of phase delay is a quarter of a period (wavelength) at any frequency. The amount of time delay it takes to move apart 90°, however, is frequency-dependent. Thus, a given time delay will produce different amounts of phase shift at different frequencies.
Phase
Acoustic propagation delay is directly related to distance, varying slightly over temperature. In air, 1.0 ms of delay corresponds approximately to 1.1 feet of distance traveled by the sound wave. So, if we know the propagation distance, then we know the time delay.

If we know the frequency, then we know the period (1/F) and the wavelength. (It helps if you can always think of frequency, period and wavelength together.

Don't just think of 100 Hz. Think of 100 Hz, 10 ms, 11 feet.) Once you visualize distance in wavelengths, then you can see how speakers will interact with each other and a room. They will add or subtract depending on the difference in number of wavelengths between the speakers or reflections at a given position.
Impedance
Specifications are a guide similar to a road map. No matter how detailed it cannot show you what you will actually see until you get there.

Another example is a list of ingredients for a recipe, again it cannot tell you how it will actually taste until you make it.

Specifications that are similar for the same size musical instruments or speakers do not tell you which sounds best. You actually have to listen. Large speakers and musical instruments suit low frequencies and vice versa

A speaker and most musical instruments have a limited frequency response and only accurate within a certain range

Look for an indication of whether the rated impedance is the "nominal" rating or the minimum impedance rating. This will be very important where devices will be connected in parallel, the amplifier will see the minimum, not the nominal load impedance when it is called upon to deliver high output in that portion of the bandwidth.
Impedance
These three impedance plots are from large format high frequency drivers mounted on their companion high frequency horns.
Impedance
Impedance varies over frequency

Most notable is the “bass hump” located at the system resonant frequency. Other dips/peaks due to inductive/capacitive elements in the crossover
and drivers

A bass-reﬂex enclosure significantly lowers the impedance at the bass port resonant frequency but introduces a peak at the bass driver free-cone resonant frequency

Lower resistance: Harder to drive, draw more current
Higher resistance: Easier to drive, draw less current but less power
Impedance
Efficiency or Sensitivity
A speaker and most musical instruments have a limited frequency response and only accurate within a certain range

Look for an indication of whether the rated impedance is the "nominal" rating or the minimum impedance rating. This will be very important where devices will be connected in parallel, the amplifier will see the minimum, not the nominal load impedance when it is called upon to deliver high output in that portion of the bandwidth.
Efficiency or Sensitivity rating
We specify sensitivity of a loudspeaker in terms of dB SPL for 2.83 V input.The sound pressure level is measured on-axis in anechoic conditions at a distance of 1 metre from the loudspeaker.

2.83Volts corresponds to the voltage across a standard 8 speaker driven at 1Watt.

How is this the case referring to Power formula?
Efficiency or Sensitivity rating
So if we measure 0.2 Pa at one volt what is the Loudspeakers Sensitivity in dB?
Efficiency or Sensitivity rating
Power = (Voltage)2/ Impedance

Determine if the sensitivity rating is based on a specified signal voltage at either the rated or nominal impedance, it makes a difference. Where minimum impedance is lower than nominal, and the test signal bandwidth includes the minimum impedance point, it can skew the sensitivity rating.

P = (2.83V)2 / 8 ohms = 1 watt
P = (2.83V)2 / 6.8 ohms = 1.17 watts ( +0.7 dB)
P = (2.83V)2 / 5.5 ohms = 1.45 watts ( +1.6 dB)

Quick check of ratio of impedance
10log (8 ohms / 6.8 ohms) = 0.7dB
10log (8 ohms / 5.5 ohms) = 1.6dB
Power Handling
Power handling is one specification that has been widely interpreted by various manufacturers. A variety of measurement methods has led to some lack of clarity as to the relevance of each rating.
Power Handling
We specify sensitivity of a loudspeaker in terms of dB SPL for 2.83 V input.The sound pressure level is measured on-axis in anechoic conditions at a distance of 1 metre from the loudspeaker.

2.83Volts corresponds to the voltage across a standard 8 speaker driven at 1Watt.

How is this the case referring to Power formula?
So if we measure 0.2 Pa at one volt what is the Loudspeakers Sensitivity in dB?
Power Handling
Sensitivity combined with power handling will tell you what the maximum output level capability is. A high efficiency device with low power handling may not be able to produce as high an output level as a low efficiency device with higher power handling, and vice versa.
AES power ratings are a good indicator of thermal and mechanical survivability where the program material is generally uniform in its spectrum content.

Because this measurement is based on long term 24 hour power handling, it will also incorporate the effects of the change in impedance that occurs with heating of the voice coil (power compression). This power rating may not disclose the mechanical limits of the device when used with highly transient signals.
Power Handling
The AES2-1984 standard - This is a standard for loudspeaker components by the Audio Engineering Society.

It is very commonly used, and, although meant for components, it is also often used for individual ways of an active system. It specifies a 6 dB crest factor pink noise signal, with a bandwidth of one decade.

For example, a bass loudspeaker could use a 50-500 Hz band, whereas a high frequency unit could use 1000-10000 Hz.

The illustration shows the spectrum of both AES signal spectrum examples. The duration of the test is 2 hours, after which the component should not show appreciable damage.
Speaker 1
Sensitivity: 95dB @ 1 watt @ 1 metre
Power handling: 300 watts AES
300 watts is 24.8 dB above 1 watt
Max output: 95dB + 24.8dB = 119.8dB @ 1 metre

Speaker 2
Sensitivity: 99dB @ 1 watt @ 1 metre
Power handling: 150 watts AES
150 watts is 21.8dB above 1 watt
Max output: 99dB + 21.8dB = 120.8dB @ 1 metre

Speaker 3
Sensitivity: 90dB @ 1 watt @ 1 metre
Power handling: 1000 watts AES
1000 watts is 30dB above 1 watt
Max output: 90dB + 30dB = 120dB @ 1 metre
Thermal and Mechanical Failure
The causes for thermal failure are :

too much (average) input power
excessive power outside the speaker bandpass (radio frequency, subsonic frequencies, deep bass ...). Energy not to converted to sound ends up as heat
amplifier clip, the most common cause of thermal failure
direct current (DC) at the amplifier output, although this is uncommon in today's amplifiers, which feature DC protection
excessive equalization on the ends of the bandpass, mostly high frequencies, since these frequencies exhibit low transducer efficiency and generate lots of heat. Extreme gain settings on ubiquitous basic LF and HF shelving EQ (or the "U" shape in a graphic equalizer) will make thermal failure more likely when the speaker is being driven hard

To prevent thermal failure, avoid amplifier clip, use LF and HF shelving EQ in moderation, and ensure that the speaker is only receiving frequencies within its bandpass, using high-pass and low-pass filters to limit the frequency content being fed to the speaker.

The causes for mechanical failure are always linked to excessive diaphragm (cone) movement. The speaker shows greater excursion (backward and forward movement) the lower the frequency. Hence a signal low enough in frequency and large enough in level may cause the voice coil to exit the gap, resulting in the coil rubbing, and possible ending up shorting or opening. The worst case scenario happens when the coil former hits the bottom pole piece ("bottoms out") and gets deformed. To prevent mechanical failure, avoid using signals below a speaker's bandpass, and use an amplifier of the correct power output.
Sound Systems
Loudspeaker Design
Driver
The construction of speakers is approached in the same way as musical instrument making. Fine tolerances and attention to detail make large differences to performance.

Large musical instruments and speakers suit low frequencies and vice versa. Each speaker and instrument can only function efficiently with linearity within 3 octaves (octave is ratio 1:2). Theoretically a single speaker would have to change diameter from (1in – 24ft) (20mm – 8m) to maintain similar level and dispersion over the frequency spectrum.
Driver design
The majority consist of paper or plastic moulded into a cone shape, loosely suspended in a frame so as to easily move back and forth to vibrate the air. Glued to the back of the cone is a coil of wire (voice coil) within a strong magnet field. Passing electricity through wire causes a magnetic field around the wire, which attracts or repels, causing the cone to move back and forth. The larger the magnet and voice coil the greater the power and efficiency if well made. Externally vibrating the cone will cause the voice coil to generate electricity. A speaker can work well as a microphone especially for bass drums.
Driver design
The energy of the magnet is conducted through the mild steel pole plates and pole piece and concentrated (north – south) across the gap. Hopefully the voice coil has been perfectly centred in the gap. The clearances are very very small. The smaller the gap – the more intense the magnetic field – the greater the efficiency. The slightest variations in alignment during manufacture, cause large variations in performance. No two speakers or musical instruments can be identical.
Voice Coils
Passing electricity through wire causes a magnetic field around the wire. Changing polarity of the electric current through the wire also changes the polarity of the magnetic field created around the wire. The interaction of the two magnetic fields, causes the voice coil to be pushed out of the gap forward or backward, depending on the polarity of the electricity through the voice coil.
Voice Coil length
At bass frequencies the voice coil has to move back and forth a long distance, especially at high power, compared to the high frequencies. During movement, the % of voice coil in the gap must remain constant.

The voice coil can be long and the pole plate thin or the voice coil short and the pole plate thick to achieve the same outcome. There are argued advantages and disadvantages both ways. Mid and high frequency speakers cones only move a small distance, compared to the large movement of bass speakers. The voice coil length and pole plate thickness are similar.
Voice Coil diameter
On the same diameter speaker a small voice coil has less control over the cone compared to a large voice coil. With a small voice coil the cone is able to be more resonant compared to the same size cone with a large voice coil.

Some small voice coil speakers may appear to be more efficient but this extra efficiency may be only at the one resonant bass note. At frequencies above this resonant bass note the speaker may be less efficient compared to the same cone with a larger voice coil. Cost and performance of speakers increase with voice coil size.
Cabinet Design
Cone type low frequency drivers are nearly always mounted in enclosures. The reason for this practice is illustrated in the diagram, which shows a cone driver reproducing a low frequency sine wave in free space.

In the first half cycle of the sine wave, the cone moves forward. A compression front is generated at the front of the diaphragm, with a corresponding rarefaction at the rear. The compressed air flows to the low-pressure zone at the back of the driver, in an attempt to equalize the air pres- sure. On the second half-cycle, the reverse occurs. The result is that most of the sound wave is cancelled and very little acoustic energy is generated, even though the excursion of the cone may be very long.
Directional Characteristics
At low frequencies, where the wave- length is long compared to the size of the cone, the driver is omnidirectional, as indicated in (a).
As the frequency rises, the wave- length gets shorter, and the directional pattern of the cone very gradually narrows.

When the wavelength is equal to the cone diameter, the directional pattern is as shown in Figure (b). Note that the cone is now fairly directional: 45 degrees off axis, the level is approximately 6 dB lower than it is directly on axis.

At higher frequencies, the cone's directional pattern narrows very sharply. In Figure (c), the wavelength is half the diameter of the driver diaphragm; note that the driver is now highly directional. The beamwidth will continue to narrow as the frequency rises.
Baffle function
This cancellation effect only occurs at low frequencies. At higher frequencies, the diaphragm moves very quickly, and the wavelengths are short compared with the distance to be traveled around the driver. There is not enough time for the air to travel the distance around the diaphragm, and little or no cancellation occurs.

By mounting the driver in a baffle, as illustrated in the diagram, we can increase the distance from one side of the driver to the other and thus minimize the cancellation. The larger the baffle, the longer the wavelength must be for cancellation to occur. Make it large enough, and the cancellation is entirely eliminated.

In practical loudspeakers, the baffle's function is assumed by the enclosure. The most common low-frequency enclosures used in sound reinforcement are the vented and the horn loaded enclosure.
Directional Characteristics
Directional Characteristics of Cone Drivers:

The directional characteristics of a cone driver are dependent on the relationship between the size of the cone and the wavelength of the sound that the driver is reproducing. Diagrams below shows polar plots for a typical cone driver at various ratios between cone diameter and wavelength.
Reflex Port
Vented enclosures are generally used for direct radiator, low frequency systems. A direct radiator system is one in which the driver diaphragm is coupled directly to the air (i.e., it is mounted on the surface of the enclosure, without a horn in front or behind the driver).
Reflex Port
Note that the enclosure features an opening in its front surface. The opening is called a port or vent. The internal volume of the enclosure and the port form what is called a Helmholtz resonator.

A bottle is another form of Helmholtz resonator. We know that if we blow across the neck of a bottle, we can produce a tone. The frequency (or pitch) of the tone is the resonant frequency of the resonator. Ported enclosures are designed to have a specific resonant frequency.
Horns
Horns are useful for two basic reasons:

They are generally more efficient than direct radiators

They afford better control of the directional pattern of the output sound, particularly in the mids and highs
Reflex Port
In a vented enclosure, the back wave from the driver is used to reinforce the front wave at the resonant frequency, as indicated by the arrows in the diagram. The resonant system of the enclosure and port shifts the phase of the back wave by 180 degrees, so that it is in phase with the front wave.

The area of the port and the size of the enclosure may be adjusted to tune the system. Tuning determines the frequency at which the system resonates; this is the frequency range where back-wave reinforcement occurs.

We generally choose the tuning of the enclosure in order to reinforce the very low frequency response of the driver, so as to get reasonably flat, low frequency response.

The interior of vented enclosures is always lined with absorbent material, usually fiberglass batting. The batting absorbs higher frequencies that otherwise could cause cancellations when bouncing around with in the enclosure.
Horns
The basic function of the horn is to allow the vibrating element (driver diaphragm or cone) to be much smaller and move within a smaller excursion - allowing a more accurate reproduction of the waveform, while still providing substantial output.

The horn provides a form of impedance matching. It is designed to present a relatively high acoustical impedance to the driver. A horn serves to develop a wave of relatively high pressure, low air particle movement into a wave of greater volume at the mouth of the horn where it encounters the normal acoustical impedance in the open air.

This is somewhat comparable to what an electrical transformer does.
LF Horns
A horn shaped like that in Figure 9.3, if it were to be effective at a low frequency, would be unwieldy. For this reason, practical low frequency horn enclosures are often of the folded horn type. As the name implies, folded horn enclosures are constructed by folding the horn back on itself to reduce its physical size
LF Horns
LF Horns
LF Horns
LF Horns
High Frequency
In sound reinforcement, practical high frequency loudspeakers are most often horn-loaded. The drivers used at high frequencies are designed specifically to drive the high acoustical impedance found at the horn throat, and are thus called compression drivers. Figure13-14 is a cross section of a typical compression driver
HF Driver
The coil, Figure 13-14 (a), sits in the gap of a permanent magnet (b).
The diaphragm (c) is domed, rather than being a cone. The physical dimensions of the driver leave little room for excursion, but not much is needed. High frequency reproduction requires less excursion than low frequencies, and the high throat impedance of the horn also reduces the diaphragm excursion requirements.

At high frequencies, the wavelength of the sound is small compared with the diameter of the diaphragm. For this reason, the slotted structure (d) - called the phasing plug - is used to alter the diaphragm-to-horn path length of waves emanating from different areas of the diaphragm so that their phase is coherent.

Flexible wires (g) lead from the diaphragm assembly terminals to the outside connection terminals (h), located on the dust cap (i).
HF Horns
The most important attribute that we desire in a high frequency horn for sound reinforcement is a controlled dispersion pattern. The horn should distribute high frequencies over a defined angle both in the horizontal and vertical axes. To the extent that it is possible acoustically, the angle of dispersion should be consistent over the full frequency range of interest - usually, up to about 16 kHz. That way the sound quality off axis will be close to that on axis.

The horizontal and vertical dispersion angles of a typical reinforcement high frequency horn will usually differ from one another, and with good reason. We usually need a fairly wide horizontal angle in order to cover a typical audience area. A similarly wide vertical angle would waste acoustic energy by directing it to areas where we don't need or want it - into free space or onto ceilings, for example.

The loudspeaker industry seems to have settled upon horizontal angles in the neighborhood of 80 to 90 degrees, and vertical angles on the order of
30 to 40 degrees. Narrower dispersion angles are also available in some horns. Horns with narrow dispersion concentrate sound in a smaller area, and are used for long throw applications.
HF Horns
Some common types of simple, high frequency horns are: exponential, radial, and constant directivity.

Radial horns are formed by defining a flare in two dimensions, then rotating that shape through a given arc around a central origin. The rotating shape defines the surface of the horn.
HF Horns
Constant directivity (CD) horns employ compound flare rates, with different rates in the horizontal and vertical axes. Because their directional characteristics are very consistent over a wide frequency range, constant directivity horns are becoming increasingly popular in sound reinforcement. The advantage is that once coverage is computed at a given frequency, the same coverage applies at all frequencies within the range where the horn exhibits constant coverage. This simplifies system design and often improves intelligibility.
HF Horns
The design of constant directivity horns requires the throat to narrow before flaring out to the mouth, which means they are subject to increased distortion caused by air turbulence that occurs in the throat at high sound pressure levels. One of the tricky aspects of their design is to minimize this turbulence-induced distortion.

Some traditional (non CD) horn de- signs incorporate acoustic lenses to improve their high frequency dispersion characteristics. Lenses may be made of louvers (similar to Venetian blinds), or of layers of perforated metal.

Such lenses have both good and bad points. They can be effective in producing a controlled pattern, and will not normally introduce significant sound level losses. On the other hand, they can produce resonances at the lower frequencies of the horn's response, coloring the sound. In general, a well designed horn will not require a lens to produce adequate dispersion.
Sound Systems
Amplifiers & Power
Amplifiers
The audio power amplifier is a signal processing component whose function is - as its name implies - to increase the power of an audio signal.

In sound systems, the power amplifier is always the final active component in the signal chain, located just before the loudspeakers.
The Ideal Amplifier

The amplifiers gain, ( A ) should remain constant for varying values of input signal.

Gain is not be affected by frequency. Signals of all frequencies must be amplified by exactly the same amount.

The amplifiers gain must not add noise to the output signal. It should remove any noise that is already exists in the input signal.

The amplifiers gain should not be affected by changes in temperature giving good temperature stability.

The gain of the amplifier must remain stable over long periods of time.
Classes of Amplifier
Audio power amplifiers are classified in an alphabetical order according to their circuit configurations and mode of operation. Amplifiers are designated by different classes of operation such as class "A", class "B", class "C", class "AB", etc.

These different Amplifier Classes range from a near linear output but with low efficiency to a non-linear output but with a high efficiency. No one class of operation is "better" or "worse" than any other class with the type of operation being determined by the use of the amplifying circuit. There are typical maximum efficiencies for the various types or class of amplifier, with the most commonly used being:
Classes of Amplifier
Class A Amplifier - has low efficiency of less than 25% but good signal reproduction and linearity.

Class B Amplifier - is twice as efficient as class A amplifiers with a maximum theoretical efficiency of about 70% because the amplifying device only conducts (and uses power) for half of the input signal.

Class AB Amplifier - has an efficiency rating between that of Class A and Class B but poorer signal reproduction than class A amplifiers.

Class D Amplifier - have the potential for very good efficiency (due to the fact that the semiconductor devices are ON or OFF in the power stage, resulting in low power dissipation in the device as compared to linear amplifier classes), therefore they are much lighter!
Class A
Class A Amplifier operation is where the entire input signal waveform is faithfully reproduced at the amplifiers output as the transistor is perfectly biased within its active region, thereby never reaching either of its Cut-off or Saturation regions. This then results in the AC input signal being perfectly "centered" between the amplifiers upper and lower signal limits.

In this configuration, the Class A amplifier uses the same transistor for both halves of the output waveform and due to its biasing arrangement the output transistor always has current flowing through it, even if there is no input signal. In other words the output transistors never turns "OFF". This results in the class A type of operation being very inefficient as its conversion of the DC supply power to the AC signal power delivered to the load is usually very low.
Class A
Generally, the output transistor of a Class A amplifier gets very hot even when there is no input signal present so some form of heat sinking is required.

The DC current flowing through the output transistor when there is no output signal will be equal to the current flowing through the load.

Then a pure Class A amplifier is very inefficient as most of the DC power is converted to heat.
Amplifier Classes
So the Class-A amplifier is working flat out even when there is no signal!

A Class-A amplifier can only ever be 25 percent efficient, according to the mathematics. So even working at its best, three quarters of the input power is wasted.
Class B
Class B provide an alternative strategy, in the form of a push-pull amplifier output stage.

One transistor 'pulls' the voltage up on the positive half-cycle of the waveform.

The other transistor 'pushes' the voltage down on the negative half-cycle.
Class B
Unlike the Class A amplifier mode of operation above that uses a single transistor for its output power stage, the Class B Amplifier uses two complimentary transistors (an NPN and a PNP) for each half of the output waveform.

One transistor conducts for one-half of the signal waveform while the other conducts for the other or opposite half of the signal waveform. This means that each transistor spends half of its time in the active region and half its time in the cut-off region thereby amplifying only 50% of the input signal.
Class B
In a class B amplifier, no DC current is used to bias the transistors, so for the output transistors to start to conduct each half of the waveform, both positive and negative, they need the base-emitter voltage (Vbe) to be greater than the 0.6v required for a bipolar transistor to start conducting.

Then the lower part of the output waveform which is below this 0.6v window will not be reproduced accurately resulting in a distorted area of the output waveform as one transistor turns "OFF" waiting for the other to turn back "ON". The result is that there is a small part of the output waveform at the zero voltage cross over point which will be distorted. This type of distortion is called Crossover Distortion.
Classes
Class AB
The Class AB Amplifier is a compromise between the Class A and the Class B configurations above. While Class AB operation still uses two complementary transistors in its output stage a very small biasing voltage is applied to the Base of the transistor to bias it close to the Cut-off region when no input signal is present.

An input signal will cause the transistor to operate as normal in its Active region thereby eliminating any crossover distortion which is present in class B configurations. A small Collector current will flow when there is no input signal but it is much less than that for the Class A amplifier configuration. This means then that the transistor will be "ON" for more than half a cycle of the waveform. This type of amplifier configuration improves both the efficiency and linearity of the amplifier circuit compared to a pure Class A configuration.
Class AB
The input signal now only has to twitch and the transistors will respond. This is a simplification of a real-world circuit, but only slightly so. In a real circuit, the voltages on the bases of the transistors would have to be slightly further apart, and adjustable to set the 'quiescent current' (the constant current when no input signal is present).

The benefit here is that crossover distortion is almost eliminated, at the expense of a slight standing current when the signal is at zero level.
The class of operation for an amplifier is very important and is based on the amount of transistor bias required for operation as well as the amplitude required for the input signal.

Amplifier classification takes into account the portion of the input signal in which the transistor conducts as well as determining both the efficiency and the amount of power that the switching transistor both consumes and dissipates in the form of wasted heat.
Class D
In Classes A, B and AB, the problem is lack of efficiency. Some power is wasted, and we would prefer that it could be sensibly employed in driving the loudspeakers to ever-higher sound pressure levels — or, at least, not converted to heat. Where power is wasted is where a transistor is in partial conduction.

When a transistor is fully conducting, it's like a piece of wire, and a piece of wire loses hardly any power. When a transistor is fully off, it doesn't conduct at all, and if it doesn't conduct at all, there's no power to waste. It's the in-between stages that cause the problem, where the transistor wastes power and gets hot. So what if we could find a way for transistors to be used only in their fully-on or fully-off states. If that were possible, no power would be lost.
Class D
Class D amplifiers, although there are a number of different design variations, are essentially switching amplifiers or Pulse Width Modulator (PWM) designs.

The incoming analog audio signal is used to modulate a very high frequency PWM carrier that works the output stage either fully on or off. This ultra-high frequency carrier must be removed from the audio output with a reconstruction filter so that no ultra-high frequency switching components remain to corrupt the audio signals. As previously mentioned, Class D designs are extremely efficient, typically in the range of 85% to 90% or more.
Class D
But how is the pulse waveform produced? OK, it isn't simple, but it isn't rocket science either. First we need a circuit building-block known as a comparator. A comparator has two inputs: let's call them Input A and Input B. When Input A is higher in voltage than Input B, the output of the comparator will go to its maximum positive voltage. When Input A is lower in voltage than Input B, the output of the comparator will go to its maximum negative voltage.

One input (Input A in my example) is supplied with the signal to be amplified. The other input (Input B) is supplied with a precisely generated triangle wave. When the signal is instantaneously higher in level than the triangle wave, the output goes positive. When the signal is instantaneously lower in level than the triangle wave, the output goes negative. The result is a chain of pulses where the pulse width is proportional to the instantaneous signal level.
Specifications
Breaking down the specifications for amplifiers
Output Power
This states how many watts per channel (or mono bridged) the amplifier can output into a specified load. In reality, almost all amps will put out more than their rated power output. When an amp is rated for power output, the design is such that all production amplifiers will meet this rating. To guarantee that this occurs, the ratings are on the conservative side
THD
All amplifiers are generally rated for Total Harmonic Distortion (or THD), usually at full power output, with both channels driven, over a given frequency band (normally 20-20,000 Hz) and with a particular load. Good values are anything less than 0.5 % THD. Some amplifiers have vanishingly low THD ratings, like 0.01%, this is superb but in practice it does not really need to be this low for music reproduction).

When an amplifier is measured for THD, a pure tone is applied to the input and the output is measured with special test equipment. The energy of the pure tone is measured, and the energy of the harmonics is measured. Those two values are compared, and a THD rating is calculated. A THD rating of 1% means that the total energy of all the harmonics combined is one one-hundredth of the energy in the fundamental.
Gain / Sensitivity
Gain: The amount by which the incoming signal is amplified is given in decibels (dB). Every 6dB of gain equates to a doubling of voltage; as such, a hypothetical amplifier with a voltage gain of 30dB will increase voltage by 2^5, or by a factor of 32.

Sensitivity: The max input signal voltage that drives the amp at max output
power it depends on the internal circuitry and gain of the amp, most amp are
designed to work with sensitivities in the range of o.7v to 7.5v
In the case of this amp spec:

1400 Watts x 8 Ohms = 11200
Square root of 11200 to find Voltage = 105.8
105.8 / 4.9 = 21.59
Log 21.59 = 1.33
1.33 x 20 = 26
Slew / Damping
Slew Rate: This is a term used to describe how quickly the output of an amplifier can track its input. Slew Rate is usually measured in V / usec. The higher the value (up to a point), the better the amp is at potentially reproducing the subtle nuances and dynamics associated with music reproduction.

Damping Factor: This is a quantity which defines how quickly the amplifier can stop a reproduced frequency such as a bass note. The higher the damping factor, the better the amp will control the woofer and help reduce overhang distortion (again to a point). The damping factor of an amplifier is mostly dependent on the output impedance of the power amplifier and the ability of the power supply which feeds the power amp.
Sound Systems
Crossover
Crossovers
You will find crossovers as passive devices inside a ‘‘full-range’’ speaker cabinet, as stand-alone units, and as part of a speaker processor. All serve the same purpose—to split source audio into multiple signals based on frequency.

In a full-range cabinet, the crossover really just serves the purpose of protecting the high-frequency driver. The signal enters the cabinet and is split in two (or three in the case of a three-way cabinet), and a network of old-school passive electrical components (you know, resistors, capacitors, transformers?) keep the low-frequency parts of the signal from reaching the high-frequency driver.
Passive Crossover
Inside the cabinet, the crossover splits that complete signal up into the appropriate number of bands to feed the bass elements to the bass driver, the high-frequency elements to the tweeter, and possibly the mid range to one or more mid-range drivers. In high-quality PA, monitoring and hi-fi systems, those passive crossovers can be very complicated affairs, with a lot of components employed to create the required filter responses with the correct amplitude and phase corrections.
Making it a bit confusing for some is the fact that one major audio manufacturer has a line of processors called DriveRack. So just to be clear, we will be looking at each of these processes as though each was handled by a separate piece of gear. Yes, that idea is hopelessly outdated, but I find it the best way to make sure that inexperienced sound techs really understand each process.
Passive Crossover
If inductors are used, the magnetic fields they produce can interact with each other, so they have to be spaced apart and oriented carefully to minimise that interaction.

There is also the possibility that the heat and mechanical vibration that is inherent inside the speaker cabinet can cause microphony within the crossover circuitry (ie. a sensitivity to sound that creates distortions), so the construction and installation of the crossover is not trivial either — particularly in high-powered systems.
Passive Crossover
On the other hand, some passive crossover designs are incredibly simple, particularly at the budget end of things where keeping the cost as low as possible is the primary design focus. A surprising number of simple systems rely on little more than a single capacitor to remove some of the bass from the treble driver's signal, for example.
Passive Crossover
That kind of approach obviously can't do much to smooth the integration between drivers, but it will offer some protection to the HF driver, which is likely to be unable to accommodate the bass energy without failing. If the two drivers are chosen carefully so that their natural frequency responses complement each other well, there is no reason why the sound quality shouldn't be good, even with this very simplistic approach.

So, in simple applications, a passive crossover is, without doubt, the cheapest solution, and with careful design can still deliver very good results. But the power handling is limited by the capability of the individual components, and the ideal integration of drivers may be limited because of the practical design limitations of passive crossovers — the circuitry quickly becomes very complex as the number of filter bands increase, and the expense increases exponentially.
Crossover slopes
A capacitor is an electronic component that passes high frequencies (the passband) and blocks low frequencies (the stopband); an inductor does just the opposite: it passes low frequencies and blocks high frequencies.

But as the frequency changes, neither component reacts suddenly. They do it gradually; they slowly start to pass (or stop passing) their respective frequencies. The rate at which this occurs is called the crossover slope.

It is measured in dB per octave, or shortened to dB/octave. The slope increases or decreases so many dB/octave. At the simplest level, each component gives you a 6 dB/octave slope (a physical fact of our universe).
Crossover slopes
Again, at the simplest level, adding more components increases the slope in 6 dB increments, creating slopes of 12 dB/oct, 18 dB/oct, 24 dB/oct, and so on.

The number of components, or 6 dB slope increments, is called the crossover order. Therefore, a 4th-order crossover has (at least) four components, and produces steep slopes of 24 dB/octave.

The steeper the better for most drivers, since speakers only perform well for a certain band of frequencies; beyond that they misbehave, sometimes badly. Steep slopes prevent these frequencies from getting to the driver.

You can combine capacitors and inductors to create a third path that eliminates the highest highs and the lowest lows, and forms a mid-frequency crossover section. This is naturally called a 3-way system.
Crossover Filters
These days, when confronted by a digital speaker processor or digital crossover, you have multiple choices in the high pass, low pass and crossover filter selections. For those not up on filter lingo, words like Butterworth, Bessel, and Linkwitz-Riley sound more like European law firms than filter types.
Crossover Filters
Most typical speaker processors offer choices like: Butterworth 12, 18 and 24; Bessel 12, 18 and 24; and Linkwitz-Riley 24. These labels indicate the filter type name and the db/octave filter steepness in the “stop-band.” Tendency to fall into convention and choose Linkwitz-Riley filters at the crossover frequencies, and select 12dB/octave Butterworth filters for the low cut and high cut points (e.g. 45Hz and 16kHz, respectively).

The frequency associated with the filter is typically at its 3dB point. For our general discussion of stop filters for speaker processing, the -3dB point usually denotes the filter’s corner frequency.
Butterworth
A “maximally flat amplitude” type of filter.

Butterworth filters do their best to keep a reasonably sharp but smooth drop at the filter corner frequency, at the expense of letting the phase response wander a bit. Most filters are characterized by their behavior when exposed to impulses of signal (spikes), transient steps in signal (step response), and how much phase delay the filter imposes on signals in various parts of the passband and stopband (group delay).
Butterworth
Butterworth filters in the two- to four-pole variety have slightly more phase change than Bessel filters, and are more prone to ring (dampen less) with impulses and transient steps.

Application-wise, Butterworth filters are pretty much the default choice of the far ends of the audio spectrum to ensure out-of-band signals roll quickly off.

Because the phase shifts are more dramatic, you are less likely to use Butterworth filters at crossover points. There are exceptions, as you will see in the Linkwitz-Riley description. But if you want a 90-degree shift at the corner frequency, a two-pole Butterworth filter is your ticket.
Bessel Filter
Bessel filters are the natural opposite of Butterworth filters, in that Bessel filters are described as “maximally flat delay.” This means the amount of phase shift in the passband to stopband is minimized compared to other filters. Also,

Bessel filters have more dampening (less ring) when exposed to impulses
and step transients. Compared to a Butterworth, a Bessel filter has a noticeably less sharp corner in transition from passband to stopband.
Bessel Filter
Bessel filters are best used is applications where crossover points require minimal phase change from one driver to another. However, Bessel filters are the least used filter since the Linkwitz-Riley filter came about in 1976.

Bessel filters are still available, but used much less these days. If you suspect you have too much ringing in your Butterworth filters, switch to Bessel filters to stomp out that problem.
Mr. Linkwitz and Mr. Riley are two electrical engineers who worked for Hewlett-Packard back when it was a dominant test equipment manufacturer, not the printer and computer maker it is today. The Linkwitz-Riley filter concept came from cascading pairs of identical two-pole Butterworth filters in low pass and high pass configurations.

The result is a crossover filter that uses the same corner frequency in high pass and low pass, has no peaks or dips and is phase continuous at the crossover frequency. In other words, at the crossover frequency, both drivers are in phase, each contributing half the energy they would in their passbands.
Before Linkwitz-Riley filters, the Butterworth and Bessel filters would result in the drivers’ differing phase motions and peaking in amplitude response as both drivers contributed more fully at the crossover frequency. Since the birth of Linkwitz-Riley filters and modern analogue “active” filters, almost all analogue crossover units use the 24dB/octave Linkwitz-Riley filters at each crossover point.

With the new DSP speaker processors, many analogue circuits and quad-matched potentiometers are now replaced by a digital math equation that creates all these filter types with perfection never dreamed of 30 years ago.
It uses cascaded pairs of Butterworth filters in combination to achieve -6dB attenuation at the crossover point in each of the High-pass and Low-pass filters which achieves a summed magnitude response which is completely flat.

Not only that, the phase response is identical between the two filters so that the phase difference between adjacent drivers is identical, so the polar response is rock-steady, producing a main lobe which is precisely at 0 degrees.
Because of the way the constituent Butterworth filters are combined, Linkwitz-Riley alignments are all even-order. This diagram shows the Magnitude response of different Orders of Linkwitz-Riley alignment.
Active Crossovers
So, for more demanding applications — either in terms of the number of bands needed, or for more precision, or to increase the power handling capability (or even all three) — active crossovers tend to be the norm.

An active crossover does the same basic job as a passive crossover, but instead of receiving as its input the full-band, high-power signal from an amplifier and dividing it passively between the various drivers, it works on the original line-level signal that would previously have been fed to the power amp.
Active Crossover
The line-level input signal is divided into two or more band-filtered signals using active equalizer stages. Active crossover networks are designed to be inserted in the signal chain before the power amplifier.They thus work at far lower signal levels (milliwatts) than do passive, high level crossovers (hundreds of watts).

These filter stages still use resistors, capacitors and (often) inductors, but the use of active gain stages as part of that circuitry enables the overall design to provide far greater precision and flexibility in creating the required amplitude and phase responses, while also maximising the independence of one section from all the others.

In some cases, a degree of time alignment can also be built in to help correct for the different acoustic centre positions of the different drivers, too.
Active Crossover
A better solution is to employ co-axial drivers in which the tweeter element is physically mounted inside the woofer, so that everything radiates from more or less the same acoustic centre.

Tannoy are well known for this approach, but it is expensive and brings its own set of compromises and issues. The electrical solution is to introduce phase shifts (or very short time delays) in the active crossover, to help correct the mechanical alignment errors by controlling the relative time that signals are emitted from each driver.
Active Crossover
For example, the acoustic centre — the point where the sound waves appear to radiate from — of a large moving-coil bass driver is typically between 10 and 20 centimetres behind the cabinet baffle.

In contrast, the acoustic centre of a soft-dome tweeter may be less than one centimetre behind the baffle. As a result, different frequency components of a sound source will appear to radiate from different spatial positions — and that will affect stereo imaging precision, amongst other things.

This mechanical problem can be corrected by mechanical means, for example by employing a stepped baffle to set the tweeter back onto the same source plane as the woofer — but that then introduces other problems such as diffraction at the baffle discontinuities
Active Crossover
Active crossover networks require a power supply to operate and come packaged in single-space, rack-mount units or more often in recent years, built into loudspeakers with power amplifiers.

There are no amplifier power loss problems, since active circuits operate from their own low voltage power supplies. And with the inefficiencies of the passive network removed, the power amps more easily achieve the loudness levels required.
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