Physics 116 2017
Wave Motion
Tues. 4/11, Thurs. 4/13
What is a wave
A WAVE is a vibration or disturbance in space.
A MEDIUM is the substance
that all SOUND WAVES travel
through and need to have in
order to move.
Mathematical modeling
f(x) = sin(x)
Does this function alone accurately model this
wave?
Traveling sine waves
• First adjustment: introduce time
– f(x, t) = sin(x - t)
• Second adjustment: Make the units work
– f(x, t) = sin(kx – ωt)
• Now the units inside are dimensionless– exactly what sine needs
• Final adjustment: Add a constant to make the model
work for any wave
– f(x, t) = A sin(kx – ωt)
• This describes the vertical displacement of the
particles that make up the medium
Two types of Waves
Two types of Waves
The first type of wave is called Longitudinal.
Longitudinal Wave - A fixed point will move parallel with the wave motion
2 areas
Compression- an area of high molecular density and pressure
Rarefaction - an area of low molecular density and pressure
Two types of Waves
The second type of wave is called Transverse.
Transverse Wave - A fixed point will move perpendicular with the wave motion.
Wave parts(recall demo for simple harmonic motion )- crest, trough,
wavelength, amplitude, frequency, period
Wave Speed
You can find the speed of a wave by multiplying the
waves wavelength in meters by the frequency (s-1 or
Hz); this gives you the wave speed in meters/second.
speed = distance / time
= wavelength / period
= wavelength * frequency
Example
A harmonic wave is traveling along a rope. It is observed that the
oscillator that generates the wave completes 40.0 vibrations
in 30.0 s. Also, a given maximum travels 425 cm along a rope
in 10.0 s . What is the wavelength?
cycles 40
f 

 1.33 Hz
sec
30
x 4.25
v

 0.425 m/s
t
10
vwave
vwave  f   
 0.319 m
f
A wave travels one meter each time the
oscillating source comes back to its highest
position. Which of the following makes
sense?
1. =1 m and v=1 m/s
2. =2 m and v=1 m/s
3. =1 m and v=2 m/s
4. =2 m and v=2 m/s
5. None of the above make sense
A wave travels one meter each time the 2 Hz
oscillating source comes back to its highest
position. Which of the following makes
sense?
1. =1 m and v=1 m/s
2. =2 m and v=1 m/s
3. =1 m and v=2 m/s
4. =2 m and v=2 m/s
5. None of the above make sense
• For a transverse wave disturbance, describe how
particles in a medium move with respect to the wave’s
direction of travel.
• For a longitudinal wave disturbance, describe how
particles in a medium move with respect to the wave’s
direction of travel.
Two types of Waves
• For a transverse wave disturbance, describe how
particles in a medium move with respect to the wave’s
direction of travel.
For a transverse wave, particles in the medium are displaced
perpendicular to the direction of the wave motion
• For a longitudinal wave disturbance, describe how
particles in a medium move with respect to the wave’s
direction of travel.
For a longitudinal wave, particles in the medium are displaced
parallel to the direction of the wave motion
• Using a slinky, how does shaking faster or slower impact the wave?
– My arm is the “source”, and the rate at which I shake my arm corresponds to
the frequency of the wave (shakes per second)
• How does shaking with greater intensity or lesser intensity change
the wave?
– My arm extends to greater maximum displacement or lesser maximum
displacement, varying the amplitude.
– This is the same as a pendulum going very high at its highest point, or not very
high, or a spring stretched far from its equilibrium versus one stretched only a
little bit from its equilibrium.
• Using a slinky, how can I make a wave travel with greater velocity?
Lesser velocity?
– How does velocity in air compare with in steel, or in water? How can you tell if
a train is approaching from very far away? Speed depends on the medium!
– 𝑣=
𝑇
𝜇
, T is tension in the string, 𝜇 is the mass density (mass divided by
length). We can change a string medium by changing its tension or its density
The drawings represent snapshots taken of waves traveling to the
right along strings. The grids shown in the background are identical.
The waves all have the same speed, but their amplitudes and
wavelengths vary. Rank the frequency of the waves.
A.
B.
C.
D.
E.
B>A>D>C
B>A>D=C
They are all the same.
C>D>A>B
C=D>A>B
The drawings represent snapshots taken of waves traveling to the
right along strings. The grids shown in the background are identical.
The waves all have the same frequency, but their amplitudes and
wavelengths vary. Rank the speed of the waves on the string.
A.
B.
C.
D.
E.
B>A>D>C
B>A>D=C
They are all the same.
C>D>A>B
C=D>A>B
Rectangular transverse wave pulses are traveling toward each other
along a string. The grids shown in the background are identical, and
the pulses vary in height and length. The pulses will meet and
interact soon after they are in the positions shown. Rank the
maximum amplitude of the string at the instant that the positions
of the centers of the two pulses coincide.
A.
B.
C.
D.
E.
C>D>A>B
A>C>B>D
They are all the same.
A>B>C>D
A=C>B=D