Last time we ended with different types of Waves

namely

Transverse

and

Longitudinal

Now these aren't the only, but rather the most

frequent

I then wanted to move onto a mathematical section

on wave propagation.

The reason for this skip was that it fit well with our

previous description of waves.

But now we will pick it up at the end of the lecture.

Energy in a wave.

A wave carries energy.

Think of a tsunami. There is no question

about energy there.

The energy the wave carries, is the energy we have been

using and solving for.

It is either found by taking the maximum potential energy

or the maximum kinetic energy.

In considering where the energy came from, it is most

often associated with the initial amplitude, thus we will

consider the potential energy.

A different term used to describe this energy being transported

is Intensity.

Intensity is not the same as energy, but they have the same

proportionality.

Consider a candle, or a speaker, or any point source.

For a candle, the light goes out everywhere, in all 3 dimensions

The intensity or energy doesn't get created or destroyed

it just gets spread out.

Think of concentric spheres.

A candle would be the same 'brightness' so long as you are the

same distance away, this makes one sphere.

Go to a different distance and it will be brighter, or dimmer.

This 'brightness' is intensity.

It is defined as power/ area.

Its units are W/m^2

If you think of the same candle, the power output is the same

you can then compare intensities at different distances.

If the distance decreases

by a factor of 3, what happens

to the intensity?

A. goes down by 9 times amount

b. goes down by 3 times amount

C. stays same

D. Goes up by 3 times amount

E. Goes up by 9 times amount

Also to note, the amplitude goes down the further away you

get from the source.

Since Intensity is proportional to amplitude squared, and inversely

proportional to distance squared

Amplitude can be considered as follows

**Reflection and transmission of waves**

**When a wave propagates it runs in to things**

This causes issues with transmission and

reflection.

This causes issues with transmission and

reflection.

**Depending on boundary conditions a wave**

gets reflected back differently.

gets reflected back differently.

Those were demonstrations of waves in one dimension

When we go to 2 or 3 dimensions

we introduce some new terms

Plane waves

Wave fronts

Shown on board.

Final thought with this section is reflection of 2 or 3 D wave

The law of reflection

Incoming ray angle is equal to outgoing ray angle.

Interference / Superposition

The principle of superposition sounds scary

all it really is, is addition.

When two waves come together the resultant waves

is the addition of the two.

This shows the concept of constructive and

destructive interference.

You'll notice these waves had the same

wavelength or frequency, so there was perfect

construction and destruction of the waves.

This is not always the case, if for example

two instruments play side by side, and

they are 'out of tune' (different frequencies)

you hear beats.

This idea of superposition

or the adding of waves,

mixed with the concept of

interference is what gives

rise to standing waves.

Standing waves

A standing wave is made up of waves moving in

opposite directions.

It is called 'standing' because the pattern that is

produced when the waves are added together

stays constant, it is a long lived or standing pattern.

We need to define some terms

Node = No movement

Antinode = largest movement

Different standing waves can be generated depending on

frequency, wavelength, velocity.

The most obvious is the wavelength

If the string is length L then I can get only specific wavelengths

to be standing.

This is because the string ends must MUST be nodes.

Here is a pictures of the first 4 wavelengths

For a given string under tension

the velocity remains constant.

Recall:

So as the wavelength changes,

the frequency changes

A particular string resonates in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will resonate.

For some unknown reason to me, we have two terms

that describe these standing waves

Harmonics

and overtones

n Harmonics overtones

1 1 fundamental

2 2 1

3 3 2

4 4 3

If my fundamental

Frequency is 100 Hz

and I produces another

standing wave that is 400 Hz

which Harmonic is it?

A. 1

B. 2

C. 3

D. 4

E. 5

Which Overtone is it?

**There are then three more sections**

Refraction

Diffraction

Wave traveling mathematically

You will do refraction and diffraction

in 106 much more intently

as for waves traveling

Refraction

Diffraction

Wave traveling mathematically

You will do refraction and diffraction

in 106 much more intently

as for waves traveling

http://phet.colorado.edu/en/simulation/fourier

For a pendulum

Velocity of traveling wave

Velocity of traveling wave on string

"Can we go over standing waves from a guitar string from the homework?"

"I don't really understand the Principle of Superposition. I don't understand the destructive and constructive interference."

If two successive overtones of a vibrating string are 280 Hz and 350 Hz. What is the frequency of the fundamental?