AP Physics B
Lesson 23 Homework Wave Motion Key
Outcomes
1. Determine the velocity, frequency, period, wavelength of traveling waves.
2. Determine the resonant lengths for standing waves on cords, open-ended air
columns, and closed-ended air columns.
3. Determine observed frequency produced by a moving sound or light source.
4. Determine the amplitude of interacting waves.
Answer
A
Number
1.
B
2.
A
3.
v  f
1
T
f
v v 
o
fo fs 

 v 
v
KEY
T
m
Question
A vibrating tuning fork sends sound waves into the air surrounding it. During the time in which the tuning
fork makes one complete vibration, the emitted wave travels

a) one wavelength
b) about 340 meters
c) a distance directly proportional to the frequency of the vibration
d) a distance directly proportional to the square root of the air density
e) a distance inversely proportional to the square root of the pressure
Two wave pulses, each of wavelength , are traveling toward each other along a rope as shown above.
When both pulses are in the region between points X and Y. which are a distance  apart, the shape of the
rope will be which of the following?
Two sinusoidal functions of time are combined to obtain the result shown in the figure above. Which of the
following can best be explained by using this figure?
(A) Beats
(B) Doppler effect
(C) Diffraction
(D) Polarization
(E) Simple harmonic motion
Use for 4-5.
D
4.
A standing wave of frequency 5 hertz is set up on a string 2 meters long with nodes at both ends and in the
center, as shown above.
The speed at which waves propagate on the string is
(A) 0.4 m/s
(B) 2.5 m/s
(C) 5 m/s
(D) 10 m/s
(E) 20 m/s
The fundamental frequency of vibration of the string is
B
5.
(A) 1 Hz
(B) 2.5 Hz
(C) 5 Hz
(D) 7.5 Hz
(E) 10 Hz
Sound in air can best be described as which of the following types of waves?
A
6.
(A) Longitudinal
(B) Transverse
(C) Torsional
(D) Electromagnetic
(E) Polarized
The figure above shows two wave pulses that are approaching each other. Which of the following best
shows the shape of the resultant pulse when the centers of the pulses, points P and Q. coincide?
A
B
7.
8.
One end of a horizontal string is fixed to a wall. A transverse wave pulse is generated at the other end,
moves toward the wall as shown above, and is reflected at the wall. Properties of the reflected pulse
include which of the following?
I. It has a greater speed than that of the incident pulse.
II. It has a greater amplitude than that of the incident pulse.
III. It is on the opposite side of the string from the incident pulse.
a) I only
b) III only
c) I and II only
d) II and III only
e) I, II, and III
A periodic wave travels through a rope, as shown in the diagram below.
A
9.
As the wave travels, what is transferred between points A and B?
A) energy, only
B) both mass and energy
C) neither mass nor energy
D) mass, only
The diagram below represents a pulse traveling from left to right in a stretched heavy rope. The heavy rope
is attached to
light rope which is attached to a wall.
C
10.
When the pulse reaches the light rope, its speed will
A) decrease B) remain the same C) increase
Diagram I shows a glass tube containing undisturbed air molecules. Diagram II shows the same glass tube
when a wave passes through it.
D
11.
Which type of wave produced the disturbance shown in diagram II?
A) torsional B) transverse C) elliptical D) longitudinal
The diagram below represents a segment of a periodic wave traveling to the right in a steel spring.
A
12.
What type of wave is illustrated by the diagram?
A) transverse B) torsional C) longitudinal D) elliptical
As shown in the diagram below, a transverse wave is moving along a rope.
C
13.
In which direction will segment X move as the wave passes through it?
A) down, only B) up, only C) up, then down D) down, then up
The graph below represents the displacement of a point in a medium as a function of time when a wave
passes through the
medium.
B
14.
What is the frequency of the wave?
A) 0.50 Hz B) 2.0 Hz C) 0.25 Hz D) 4.0 Hz
Which graph best represents the relationship between the frequency and period of a wave?
D
15.
B
16.
As the period of a wave decreases, the wave's frequency
A) decreases B) increases C) remains the same
A
17.
A
18.
A periodic wave with a frequency of 10 hertz would have a period of
A) 0.1 s B) 100 s C) 10 s D) 1 s
Which distance on the diagram below identifies the amplitude of the given wave?
A) AB B) AC C) AE D) AD
In the diagram below, which wave has the largest amplitude?
A
19.
A) A B) B C) C D) D
What is the wavelength of the wave shown in the diagram below?
C
20.
A) 4.0 m B) 10. m C) 2.5 m D) 5.0 m
Two pulses are traveling along a string toward each other as represented in the diagram below.
D
21.
Which phenomenon will occur as the pulses meet?
A) diffraction B) reflection C) refraction D) interference
Which pair of moving pulses in a rope will produce destructive interference?
C
22.
The diagram below shows two pulses, each of length l, traveling toward each other at equal speed in a
rope.
D
23.
Which diagram best represents the shape of the rope when both pulses are in region AB?
A
24.
When an opera singer hits a high-pitch note, a glass on the opposite side of the opera hall shatters. Which
statement best explains this phenomenon?
A) The frequency of the note and natural vibration frequency of the glass are equal.
B) The singer and glass are separated by an integral number of wavelengths.
C) The vibrations of the note are polarized by the shape of the opera hall.
D) The amplitude of the note increases before it reaches the glass.
The diagram below represents a vibrating string with a periodic wave originating at A and moving to G, a
distance of 6.0 meters.
D
25.
D
26.
C
27.
Which phenomenon would occur if the waves were reflected at G and returned back to A through the
oncoming waves?
A) Doppler effect B) diffraction C) dispersion D) standing waves
Standing waves are produced by the interference of two waves with the same
A) frequency and direction, but different amplitudes
B) frequency, amplitude, and direction
C) amplitude and direction, but different frequencies
D) frequency and amplitude, but opposite directions
How many nodes are represented in the standing wave diagram below?
A) 2 B) 3 C) 4 D) 6
When the stretched string of the apparatus represented below is made to vibrate, point P does not move.
C
28.
Point P is most probably at the location of
A) maximum pulse
B) an antinode
C) a node
D) maximum amplitude
The diagram below represents a rope along which two pulses of equal amplitude, A, approach point P.
A
29.
When the two pulses meet at P, the vertical displacement of the rope at point P will be
A) 2A B) 1/2A C) 0 D) A
Which pair of pulses, moving through the same medium, will produce the pulse shown below when they
are superimposed?
C
30.
Which pair of waves will produce a resultant wave with the smallest amplitude?
D
31.
1995B6. (10 points) A hollow tube of length Q. open at both ends as shown above, is
held in midair. A tuning fork with a frequency f o vibrates at one end of the tube and
causes the air in the tube to vibrate at its fundamental frequency. Express your
answers in terms of l and fo
a.
Determine the wavelength of the sound.
=1/2 
2
b. Determine the speed of sound in the air inside the tube.
V=  f o v=2• f o
c. Determine the next higher frequency at which this air column would resonate.

 2• f o 

The tube is submerged in a large, graduated cylinder filled with water The tube is
slowly raised out of the water and the same tuning fork, vibrating with frequency f O, is
held a fixed distance from the top of the tube.
d.
Determine the height h of the tube above the water when the air column
resonates for the first time. Express your answer in terms of l
h=
/2

1998B5 (10 points) To demonstrate standing waves, one end of a string is attached to a tuning fork with frequency 120
Hz. The other end of the string passes over a pulley and is connected to a suspended mass M as shown in the figure
above. The value of M is such that the standing wave pattern has four "loops." The length of the string from the tuning
fork to the point where the string touches the top of the pulley is 1.20 m. The linear density of the string is 1.0 x 10 -4 kg/m,
and remains constant throughout the experiment.
a. Determine the wavelength of the standing wave.
1.20 m/ 2 waves = 0.6m/wave
b. Determine the speed of transverse waves along the string.
v=  f (0.6m)(120Hz)=72m/s
c. The speed of waves along the string increases with increasing tension in the string. Indicate whether the value of M
should be increased or decreased in order to double the number of loops in the standing wave pattern. Justify your
answer.

V=  f
since f is constant, in order for  to decrease, v must also decrease. M must decrease given v 
T
m
and T is the weight of M.

d. If a point on the string at an antinode moves a total vertical distance of 4 cm during one complete cycle, what is the
amplitude of the standing wave?
 Tricky question !!!! One complete cycle includes 4 trips between the midline and
either the crest or trough.

A= 1cm, it equals the displacement relative to the rest position of the medium.