PH 105

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PH 105
Waves
Dr. James van Howe Lecture 4
Photo unknown source
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Outline

• Finish coupled oscillators
• Standing waves on a string
• wavelength
• Waves
• Intro
• relation of speed, frequency, wavelength
• Sound waves
• Graphical techniques/oscilloscope

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Name the composer

• Hyden
• Beethoven
• Mozart
• Rachmaninoff

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What is the relationship between the phase of the
red and the blue?
y
time

• The red lags the blue by 180 degrees
• The red leads the blue by 180 degrees
• The red lags the blue by 90 degrees
• The red leads the blue by 90 degrees

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Velocity
The velocity of a traveling wave
For sound waves in air, if I triple the
frequency.

• The velocity triples as well
• The velocity goes down by 1/3
• The velocity does not change

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Velocity and wavelength
The velocity of a traveling wave
For sound waves in air, if I triple the
frequency.

• The velocity stays the same and the wavelength
  goes down by 1/3
• The wavelength stays the same and the velocity
  triples
• Neither changes

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Coupled Oscillations
Two mass system, two degrees of freedom, two
natural frequencies (modes of vibration)
a)
k
k
k
m
m
b)
Longitudinal modes
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Transverse Coupled Oscillations
Two mass system, two degrees of freedom, two
natural frequencies (modes of vibration)
m
m
a)
k
k
k
m
b)
k
k
k
Transverse modes
m
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Infinite many transverse modes
String is like a coupled mass/spring system with
infinite number of springs and masses (transverse
vibration)
Mode
Fundamental Mode
1
2
3


Demo Standing waves
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The moving string looks blurry, the outline looks
like
Antinode
Node
Node
A
A
N
N
N
A
A
A
N
N
N
N
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Wavelength Spatial Equivalent of Period
Wavelength, l
Displacement
Second Mode
Distance
Wavelength Changes with each mode
Fundamental Mode
l/2
If the length between ends is equal to 1.0 m, then
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Modes of a String
1.0m
How many wavelengths (spatial period) do you see?

• 1.0
• 1.3
• 1.5
• 2

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Modes of a String
1.0m
What is the wavelength for this mode?

• 1.0 m
• 0.5 m
• 1.5 m
• 0.66 m

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What does this have to do with waves?
1.0m
Really just the sum (superposition) of generated
and reflected waves
Propagating disturbance
S.H.O
Before disturbance reflects off boundary
Demo wave on a rope wave machine
Snapshot in time
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Waves
Wave Disturbance that propagates through a
medium, without the medium being transported
itself.
The stadium wave
Disturbance direction
Propagation direction
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Wave velocity
Velocity
A
Displacement, ym
Snapshot in time
Distance, x
If I sit on the crest given by the dashed line
and wait for crest A to come, I wait an amount of
time T (the period of oscillation).
It travels a distance l in a time T so the
velocity is
since
so
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Wave velocity
Quantity Units
For transverse waves on a string,
For longitudinal waves in a solid,
For longitudinal waves in a fluid (air, water),
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What does this mean?

• Tension, Elastic and bulk modulus are like
  springiness of material

Springiness
Velocity
More connection between molecules, domino effect
easier
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What does this mean?

• As density goes up, velocity goes down,
• huh?

Density
Velocity
Counterintuitive
Video Demo Helium, Sulfur Hexafluoride
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What does this mean?
Newtons law of inertia Objects at rest tend to
stay at rest, objects in uniform motion (constant
velocity) tend to stay in motion
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Numerical Comparison
Air Steel
A little off from what it should be, 343 m/s
Even though steel 7,000 times more dense than
air, its springiness is million times more
Really the springiness that helps speed density
hurts it- harder to move
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Velocity, Frequency, Wavelength
Velocity determined by the material springiness
and density
We can usually can control amplitude and
frequency of oscillation, wavelength comes along
for the ride
For waves on a string
or
Demo Standing waves
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Oscilloscope the eyes of a physicist
Scope is used to look at an electrical signal as
a function of time
We will be using transducers (ex. microphone) to
convert sound energy into electrical energy to
view on the scope
Lets go through functions together

• Trigger
• Time Sweep
• Ch1, Ch2 Gain AC, DC
• XY Mode

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Homework

• Finish reading Chapter 3
• Ch3 R4, Q7

Due at the beginning of class on Wednesday
Q Questions for thought R Review Question E
Exercise