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PH 105 11.7-11.13

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Richard Datwyler

on 11 March 2015

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Transcript of PH 105 11.7-11.13

Waves
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
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

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.

Depending on boundary conditions a wave
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
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
examples 54 56
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