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PH 105 11.9-11.16
Transcript of PH 105 11.9-11.16
Last time we ended with different types of Waves
Now these aren't the only, but rather the most
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
Intensity is not the same as energy, but they have the same
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
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
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
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.
A standing wave is made up of waves moving in
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.
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
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?
Which Overtone is it?
There are then three more sections
Wave traveling mathematically
You will do refraction and diffraction
in 106 much more intently
as for waves traveling
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?