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Waves - Light and Sound
Transcript of Waves - Light and Sound
A medium is a material through which a wave travels.
If no medium is required the waves are called electromagnetic waves. Wave Motion Visible Light Sound Waves When the frequencies of notes played at the same time have ratios that can be reduced to small numbers, for example 4 : 5 or 2 : 3, we perceive the combined sound as being fairly pleasant.
However, when the ratios of the notes involve numbers bigger than 12, for example 2 : 13 or 11 : 14, the resulting sound is harsh and unpleasant.
We describe such frequency combinations as being dissonant. Chromatic Scale The full scale of 12 notes is called the equally tempered chromatic scale.
By international agreement, the frequency of the A above middle C is 440 Hz.
The next A appearing on the keyboard will be the first harmonic of this lower note and will have a frequency of 880 Hz.
Similarly, the A below middle C will have a frequency of 220 Hz. Notes Based on twelve fundamental frequencies.
A piano keyboard shows a repeating pattern of white and black keys.
This pattern is made up of 7 or more sets of 12 keys.
The 12 keys correspond to the fundamental frequencies: 7 white keys, which are designated A, B, C, D, E, F and G, and 5 black keys, which play notes that have frequencies between those of the white keys either side of them.
The distance between adjacent keys (adjacent frequencies) is referred to as a ‘semitone’.
The white notes are referred to as ‘natural notes’, and the black keys are ‘accidentals’.
An accidental can be described as a ‘flat’ (symbol b) of the natural note one semitone above it, or as a ‘sharp’ (symbol #) of the note one semitone below it. Western music structure: A to G The term timbre is used to describe the richness of sound produced by a musical instrument.
Good timbre depends upon the ability of the instrument to produce different harmonic frequencies at once. Timbre Tone-deaf people are completely unable to distinguish between sounds differing in frequency.
Very few people are truly tone-deaf, most people lie between the two extremes and it is possible to train yourself to distinguish pitch more precisely
Some car mechanics can tell by listening to an engine, what the vibration speed is. Pitch The frequency that is produced is influenced by the mass and tension of the vocal cords. The vocal cords are flaps of ligament, they are separated by a V-shaped space called the glottis.
When you are breathing rather than talking or singing, the arytenoid cartilages in the back of the throat hold the glottis open. In this state, the vocal cords do not form audible sound waves.
When the vocal cords are short and tense, the sound produced is higher in frequency; loose and long vocal cords produce deeper sounds.
As men usually have larger throats and heavier vocal cords, their voices are usually deeper than women’s voices. Both ends of the pipe are open
Fundemental will occur where successive nodes occur at the ends of the pipe
In general, n = 2L / n Open Pipes At the closed end of the pipe the particles are not free to move, the maximum displacement of air particles occurs.
Hence an antinode will occur
The fundemental has one node and one antinode
In general, n = 4L / (2n-1) Closed Pipes Compression standing waves are formed in wind and brass instruments
All pipes have at least one open end at which particles are free to enter and leave, thus that end of the pipe has constant air pressure.
Hence a node appears at the open end
As the waves in the instrument move, their speed is equal to the speed of sound in air at that temperature, regardless of whether it is open or closed Wind and Brass Instruments The wavelength of vibration in a string is related to its length by: n = 2 L / n
For our first harmonic produced by an open string (that is, a string able to vibrate without constraints):
1 = 2 L / 1 = 2 L
For the second harmonic, where we have touched our finger lightly to the string:
2 = 2 L / 2 = L
So, we see that 2 is half the magnitude of 1 .
Therefore, as v is constant we have doubled the frequency of the note produced when we lightly touch the string. By placing your finger very lightly at a point halfway down a string, you cause the string to form a node there. As a result, the string vibrates in its second harmonic.
The note formed here will have twice the frequency of the fundamental.
The speed of a wave in a string depends on its tension, its mass and its length, all of which will be constant for a particular string on a particular instrument. Now, with v constant and v = f , we can see that if the wavelength is halved, then the frequency must be doubled. Forcing upper modes of vibration The wavelength for any mode of vibration is:
n = 2 L/n
where L is the length of the string and n is the integer number associated with the vibrational mode. This means that n = 1 for the first harmonic (fundamental), n = 2 for the second harmonic etc.
The frequency at a particular mode of vibration will always be a whole number multiple of the fundamental frequency;
fn = nf1
where n is the vibrational mode and f1 is the fundamental frequency.
The strings on a stringed instrument will usually vibrate in the fundamental vibrational mode. To force a string to vibrate in any other mode will require a little intervention. The separation between two successive nodes is /2
When a string vibrates the wavelength of the vibration will be double the length of the string L
If a string vibrates in its second vibrational mode (called the first overtone or the second harmonic) there will be two antinodes and three nodes.
The wavelength of such a vibration will equal the length of the string; that is, 2 = L.
A string vibrating in its third vibrational mode (also known as the second overtone or third harmonic) has three antinodes and four nodes, and the length of the string is now 1 ½ wavelengths long.
The wavelength at this time will be: 3= 2L/3 Contd.
Standing waves also form in air. This can happen when a sound source is directed at a reflecting surface, causing the reflected waves to be superimposed on the incident waves, or else it can occur when two sound sources that are emitting waves at the same frequency are placed facing each other.
As with transverse standing waves, the nodes formed by sound waves in a medium are points where the medium remains undisturbed. The air pressure at the nodes is normal and, if you were to stand at these locations, the sound would be significantly softer if you could hear it at all.
The antinodes are the locations in the medium that are disturbed the most, alternating between air pressure that is higher and then lower than normal. At these points, sound is particularly loud. Standing waves and sound Transverse standing waves
Standing waves occur at wave frequencies when there is interference between the initially generated waves and the reflected waves.
Where an incident wave coincides with a reflected wave that is opposite in phase, the two waves will essentially cancel each other out due to destructive interference, leaving the medium at that location undisturbed.
Standing Wave animation Standing Waves Worked Example The quality of a hall can be evaluated in terms of its reverberation time. This is usually when the echoes have a sound level intensity less than 60 dB.
Reverberation time of a space (T R) is directly related to the volume of the space (V ) and inversely proportional to its effective absorbing surface area (A): TR = 0.161 V / A
To calculate the effective absorbing surface area of a space, the effective absorbing surface of every fixture must be taken into account by assigning each of the surfaces (curtains, chairs, floors, ceiling, walls etc.) an absorption coefficient which will be slightly different for sounds of differing frequency range. The absorption coefficient is the proportion of sound that is absorbed by that surface. Glass in a window, for example has an absorption coefficient of 0.18 for 500 Hz; this means that it absorbs 18% of sound at 500 Hz which falls on it. Thick carpet, on the other hand, has an absorption coefficient of up to 0.60 — absorbing 60% of sound. Reverberation Time Reverberation time is the period of time that elapses between the incidence of a sound and the noise level of that sound’s echo dropping below 60 dB.
The reverberation time of a space depends upon its size and shape, and the nature of the surfaces and objects within it. Reverberation Time Acoustics is the scientific study of sound. Architecture and engineering, use acoustics to explain how characteristics of spaces affect sounds within them.
Surfaces, fittings and even seating of a concert hall are designed to make the music played on stage as clear as possible. Flat walls, ceilings or hard surfaces, have a tendency to cause reverberation - an effect where the audience hears a noticeable time delay between the played note ending and the dying away of that note
Soft surfaces can absorb sound, making it ‘acoustically dead’.
Soft surface used to completely soundproof. Frequency and quality of sound heard by the performer, backing musicians and sound technician are exactly the same.
Rooms are lined in heavily textured padding or bottoms of egg cartons, so no spurious reflection or resonance of sound waves. Basic acoustics The natural vibration of an object is the rate at which an object oscillates once set into motion.
The natural frequency of an object is the frequency at which it will vibrate when stimulated.
It is independent of the size of the stimulus, depending solely upon the object’s size, shape and composition.
The natural frequency is also the rate at which resonance occurs Vibrations and Resonance Worked Example Wave pulses Decibels are used to indicate how loud or soft a sound is.
A decibel is a unit used to compare the intensity of signals (sound, light, or other)
The decibel difference between two intensities is given by :
L = 10 log (I2 / I1 )
where L is the ratio of Intensity, I1 & I2 are the respective intensity of the sounds (W m-2 ) Decibels Volume or Loudness is a subjective quantity. A more measurable quantity is Intensity.
Intensity I is defined as the power passing through each square metre of the surrounding space
I = P / A where I is intensity (W m-2 Watts per square metre or Joules per square metre per second), P is the Power (W) and A is the area (m2)
The power of sound is directly proportional to the square of the waves amplitude. Sound Characteristics Sound is a mechanical wave: it needs a medium to propagate. Air particles move to create the sound. If there were no particles, kinetic energy could not be transferred, then there would be no sound.
This is why sound cannot travel in a perfect vacuum (space) Sound The rate at which a sound source vibrates is called the frequency.
This is equal to the number of complete vibrations that are made in a 1 second period of time.
The frequency of sound is measured in hertz (Hz) or cycles per second.
Frequency = 1 / Time Period (the time it takes to complete one cycle or oscillation)
The frequency of a sound wave will be equal to the frequency of the sound source. Speed of Sound What is SOUND? Noise is made up of vibrations that tend to be irregular in frequency and loudness.
A standing wave forms when waves moving in opposite directions interfere in such a way as to leave points throughout the medium undisturbed while the sections in between undergo maximum displacement.
Nodes are points on a standing wave that undergo the least disturbance, while antinodes form where the medium undergoes the most disturbance.
All musical instruments are made up of a principal vibrator and an exciter; most have a resonator.
Stringed instruments form standing waves that have a node at each end.
The nth harmonic wavelength formed by the string is related to the string length L by n =2 L / n. Summary In Western music, two notes are considered to form a harmonious sound when played together if their frequencies can be expressed as a whole number ratio. For example, two notes an octave apart are harmonious.
A note which is an octave higher than another will have twice its frequency, the frequency ratio of two notes an octave apart will be 1 : 2 — a whole-number ratio. Harmony and dissonance Certain combinations of notes sound very pleasing.
Different cultures have quite different views about what sounds pleasing!
The notes used in Western music have emerged from a long history of musical experimentation and tradition. Music The same note played on different instruments results in a markedly different sound. Middle C played on a viola has a warmer feel to it than on a trumpet.
A note gives a sound made up predominantly of vibrations corresponding to the fundamental frequency.
A number of harmonic frequencies (each of which is a multiple of the fundamental) may also be heard.
The harmonics are not as loud as the fundamental, but they contribute to the richness of the sound produced by the instrument.
Some musicians argue that the timbre of a well-constructed wooden instrument improves with age, as the passing years affect the way in which its soundbox is able to vibrate by loosening glues and hardening varnishes to produce more harmonics. Timbre - The quality that makes instruments sound different (tam-buh) Pitch gives a general indication of a sound’s frequency.
High pitch sounds are high frequency sounds.
You may have heard of musicians who have perfect pitch. This is an ability to precisely name the note associated with a heard frequency.
Previously perfect pitch was required to tune an instrument. Now, instruments are tuned electronically. Pitch and Frequency The human vocal tract approximates a closed pipe in the way that it functions, with the closed end considered to be near the eardrum.
Air is pushed through the vocal tract by the lungs and is excited into vibration as it passes the vibrating vocal cords.
The length of the pipe is controlled by the upwards or downwards movement of the larynx in the throat. The Human Voice For an instrument such as the recorder, there is a series of holes along the front which can be covered or uncovered by the fingers.
When all of the holes are covered, the vibration length of the pipe is equal to the length of the recorder.
If you uncover the bottom three holes, the length of the effective air column ends just above the first uncovered hole.
As the length is now shorter, the fundamental frequency will be increased and a higher note will be heard.
Some instruments such as the clarinet and the saxophone use keyed valves to open and close holes, thus changing the effective length of the pipe. Pipe Instruments The frequency at which a pipe vibrates and, so, the note produced depend upon the length of the pipe.
To make an instrument produce different notes, there must be some way of changing the vibrating length.
For some instruments such as the trombone or the slide whistle, this is done by allowing one section of the pipe to slide into another. Playing different notes on a pipe instrument Open Pipes A) fundemental, 1st harmonic L = ¼
B) first overtone, 3rd harmonic L = ¾
C) second overtone, 5th harmonic L = 5/4 Closed Pipes A string held under tension will produce sound. This is the basic principle from which all stringed instruments have been developed.
The Greek mathematician Pythagoras was the first to examine them from a scientific point of view. He observed that, for a string held under tension that will produce a sound, halving the length of the string while keeping the same tension causes the frequency of its vibration to double. He also found that increasing tension in the string while keeping its length constant will increase the frequency as well. Stringed Instruments All musical instruments have an exciter and a vibrator; most will also have a resonator as well.
The principal vibrator is where the initial vibration originates.
The exciter causes the principal vibrator to start or keep vibrating.
The exciter is often separate from the instrument, a drumstick or a violin bow
The resonator reinforces the vibrations of the principal vibrator. This will increase the amplitude of the vibrations and so increase the loudness of the sound produced by the instrument. Musical Instruments Sine Wave superposition
http://paws.kettering.edu/~drussell/Demos/superposition/superposition.html Animations The diagram shows the distribution of air particles and the corresponding changes in air pressure for a volume of air where a standing wave is occurring over one cycle.
Because the nodes in a standing wave are the regions of the medium that remain undisturbed, they remain at standard air pressure.
The antinodes of a standing wave correspond to regions of the medium that are disturbed the most, fluctuating between pressure that is higher and lower than standard air pressure. Sound Waves In a standing wave, these undisturbed points (called nodes) are evenly spaced.
Where an incident wave coincides with a reflected wave that is equal in phase, constructive interference occurs and the amplitudes of the two waves reinforce each other. We call these points where the medium is disturbed the most antinodes.
Violin demonstration Contd. What music is, is very subjective
One persons music is another’s noise
The line between music and noise is becoming less distinct as noises are increasingly used in music. E.g. Running water, squealing brakes etc.
If the vibrations caused by a source form simple sustained patterns with a constant frequency, we tend to identify them as musical sounds. Music The best reverberation time for a concert hall depends upon the type of performance being given. Speech sounds best in a hall that has a reverberation time of between 0.4 to 0.8 s, while halls with times of between 1.0 and 2.0 s are generally better for music. A symphony hall for a full orchestra is best with a time of between 1.7 and 2.0 s.
A performance space is considered to have good acoustics if there are no noticeable echoes, the loudness of all sounds is uniform throughout the space, and it does not allow noise from the outside world to be heard inside. General Information Resonance occurs when an object’s forced vibration is equal to its natural frequency. This has the effect of increasing the amplitude of the vibration.
Think of the opera singer and the glass or the army marching over a bridge Resonance Unlike natural vibration, forced vibration is the rate at which an object is compelled to vibrate by placing it in contact with another vibrating object.
A violin string vibrates at its natural frequency. This causes the bridge to vibrate at the same frequency and the body of the violin and the air in the body to vibrate as well. (forced)
Forced vibration is necessary for sound amplification. The sound produced by a violin string vibrating is not very loud.
The shaping of the body of a violin, the air and belly are able to produce a much larger sound at the same frequency. Forced Vibration The natural vibration of an object is the rate at which it oscillates once set into motion and is inherent to the object’s structure.
A tuning fork, when struck with a rubber hammer, will vibrate at the same rate regardless of how hard it is hit as its vibrational rate is determined by the metal it is made from, its length and the spacing of its prongs.
A tuning fork tuned to the A above middle C will vibrate at 440 Hz when struck.
As a result, we can say that this is its natural frequency. Natural Vibration Destructive Interference is the disturbance that occurs when the sum of two superimposed waves is zero
Sound sources that are in phase produce compressions at the same moment in time Destructive Interference Loudspeakers
Two speakers connected to the same source at the front of a hall. Although the speakers are in phase there are areas of the hall where the sound is loud and areas where the sound is soft. Loudspeakers Interference is the disturbance caused by the interaction of two or more waves at the same location
Constructive Interference is the disturbance caused when two waves reach a position at the same time and give rise to an amplitude which is greater than that due to each wave alone
Sound waves can reinforce each other, or cancel each other out Interference of sound waves
When sound waves hit hard surfaces, they make elastic collisions and rebound
When sound waves hit a soft surface, the surface is yielding and the rebound not so clear cut Reflection of sound Typical Values Assuming dry air.
At 0º C sound travels at 331ms-1 , but it travels at 344 ms-1 at 20º C
Increase in air humidity causes an increase in the speed of sound, but this is small and for our purposes can be ignored. Speed of Sound The general wave equation gives the speed (v) of a wave in terms of frequency (f) and wavelength ( )
v = f
T = 1 / f where T is the time period of the wave and f is the frequency
V is volume and T is absolute temperature
V1 = V2 (T1/T2 ) where T1 and T2 deg Kelvin General Wave Equation
Note the details on the wave above Wave Details A closed pipe will form a node at its open end and an antinode at its closed end. For a closed pipe of length L, n = 4 L / (2n-1)
An open pipe will form nodes at both ends. For an open pipe of length L, n =2 L / n
Pitch is a qualitative measurement of frequency.
Timbre is a qualitative measure of the complexity of sound produced by an instrument. It is dependent upon the number of harmonic frequencies that are produced.
The Western music scale is referred to as the equally tempered chromatic scale.
Two notes played simultaneously are said to sound harmonious if the ratio of their frequencies is made up of whole numbers involving numbers smaller than 12.
Notes whose frequencies form whole-number ratios involving numbers larger than 12 are said to be dissonant and are considered unpleasant. Summary Contd. pairs of notes that are considered harmonious are shown below. Harmonious Notes One full set of notes (called an ‘octave’) is made up of A, A# (also called Bb), B, C, C#/Db, D, D#/Eb, E, F, F#/Gb, G and G#/Ab. The Piano keyboard When a string is plucked, it is set in motion and standing waves are formed.
Strings on instruments are fixed at each end, nodes will always form there.
There are a number of different standing waves that can be formed in the string which have a node at each end.
(a) shows the fundemental or first harmonic (one antinode in the middle of the string)
(b) shows the first overtone
(c) shows the second overtone Vibrational Modes in a String For example, a 400 m2 wooden floor which has an absorption co efficient of 0.10 for 500 Hz sounds would have an effective absorption area equal to 400 x 0.10 = 40 m2.
The table indicates the absorption coefficients for common building materials when exposed to sound with a frequency of 500 Hz (which lies in the middle of the frequency range for the voice and for musical instruments). Examples Reflection is more effective for higher frequencies than lower frequencies due to diffraction Acoustics Destructive Interference occurs at positions where:
path difference = n / 2
Where n is an odd integer
Constructive interference occurs where n is an even number Interference
Sound waves travel outwards from a sound source in three dimensions
At x metres away from a sound source, the intensity = P/Area Sound Waves
Diagram shows wavelength, air pressure, compression and rarefaction
The top of the wave is called the crest, the bottom the trough. Particle Compression and Rarefaction
Kinetic energy is transferred from the vibrating object to the air.
When the sound waves strike the human ear the eardrum also starts to vibrate, which is picked up by structures in the ear allowing us to hear. How do we hear sound?
Sound is created when a vibrating object causes particles in the air to be alternately pushed close together and spread further apart.
This movement is known as compression and rarefaction. Together they are known as longitudinal waves or compression waves.
Together they create a series of pushes along the air The principal vibrator is the string, the exciter will be your fingers or a plectrum, and the resonator is the curved, hollow body.
Unlike the hollow body of an acoustic guitar, which allows resonance to amplify the sound of the strings, the body of an electric guitar is usually solid, so it uses a very different system to make itself heard. When its steel strings are plucked, devices mounted on the guitar’s body beneath the strings (called pickups) use electromagnetic induction to convert the vibration of the strings into electric current, which is then passed to an external amplifier. Acoustic Guitar The distance between successive compressions or successive rarefactions is called the wavelength which is represented by the symbol lambda . Wavelength is measured in metres. Wavelength Destructive Interference is the disturbance that occurs when the sum of two superimposed waves is zero
Sound sources that are in phase produce compressions at the same moment in time Destructive Interference Wave pulses Interference is the disturbance caused by the interaction of two or more waves at the same location
Constructive Interference is the disturbance caused when two waves reach a position at the same time and give rise to an amplitude which is greater than that due to each wave alone
Waves can reinforce each other, or cancel each other out Interference of waves To create a wave a disturbance has to be created in an undisturbed medium.
Each crest of a wave is called a pulse
There are transverse waves, where each point of the wave vibrates perpendicular to the direction of travel.
And compressional (longitudinal) waves, for example when a spring is compressed and let go. Waves The wave equation v = f is known as the wave equation
v is the velocity in m/s and f is the frequency in Hz. Lambda is the wavelength Shapes of lenses Lenses Light through lenses Ray diagrams The lens formula Light rays and Mirrors The ray towards the mirror is called the incident ray, the ray leaving the mirror, the reflected ray and perpendicular to the mirror is called the normal Parallel rays reflect as shown here
Smooth surface right
Irregular surface below Images Law of reflection states that the angle of incidence equals the angle of reflection Dispersion is the separation of light into a spectrum of colours as a result of refraction
Refraction is the change in direction that a light ray experiences when passing into a new medium. Colour The eye has receptors for red, green and blue spectral colours. These are known as primary additive colours as when the three colours are shone onto the same location they produce white light.
Any colour can be made from a combination of these three colours. The human eye A filter is a coloured transparent material that allows light of a selected colour to be transmitted while all other colours are absorbed. Filters A red filter will only allow red light through, similarly green and blue filters allow only their respective colours through. When shining white lite at a coloured filter, the colour and its close neighbours will pass through it. height of the image = -v height of the object u Pigments QA pigment is a substance that is coloured due to the types of chemicals that it is made from and which in turn is used to colour other materials. Pigments only reflect back certain colours while absorbing the rest.