11th Grade Midterm Workbook

1. Which of the following is not an example of 7. A mass-spring system can oscillate with simple
approximate simple harmonic motion? harmonic motion because a compressed or
a. a ball bouncing on the floor stretched spring has which kind of energy?
b. a child swinging on a swing a. kinetic
c. a piano wire that has been struck b. mechanical
d. a cars radio antenna waving back and forth c. gravitational potential
d. elastic potential
2. Vibration of an object about an equilibrium
point is called simple harmonic motion when 8. The angle between the string of a pendulum at
the restoring force is proportional to its equilibrium position and at its maximum
a. time. displacement is the pendulums
b. displacement. a. period.
c. a spring constant. b. frequency.
d. mass. c. vibration.
d. amplitude.
3. Tripling the displacement from equilibrium of
an object in simple harmonic motion will 9. For a mass hanging from a spring, the
change the magnitude of the objects maximum maximum displacement the spring is stretched
acceleration by what factor? or compressed from its equilibrium position is
a. one-third the systems
b. 1 a. amplitude.
c. 3 b. period.
d. 9 c. frequency.
d. acceleration.
4. A mass attached to a spring vibrates back and
forth. At the equilibrium position, the 10. A pendulum swings through a total of 28. If
a. acceleration reaches a maximum. the displacement is equal on each side of the
b. velocity reaches a maximum. equilibrium position, what is the amplitude of
c. net force reaches a maximum. this vibration? (Disregard frictional forces
d. velocity reaches zero. acting on the pendulum.)
a. 28
5. A mass attached to a spring vibrates back and
b. 14
forth. At maximum displacement, the spring
force and the c. 56
a. velocity reach a maximum. d. 7.0
b. velocity reach zero.
c. acceleration reach a maximum. 11. A child on a playground swings through a total
d. acceleration reach zero. of 32. If the displacement is equal on each side
of the equilibrium position, what is the
6. A simple pendulum swings in simple harmonic amplitude of this vibration? (Disregard
motion. At maximum displacement, frictional forces acting on the swing.)
a. the acceleration reaches a maximum. a. 8.0
b. the velocity reaches a maximum. b. 16
c. the acceleration reaches zero.
c. 32
d. the restoring force reaches zero.
d. 64

1
Name: ______________________ ID: A

12. For a system in simple harmonic motion, which 16. Which of the following features of a given
of the following is the time required to pendulum changes when the pendulum is moved
complete a cycle of motion? from Earths surface to the moon?
a. amplitude a. the mass
b. period b. the length
c. frequency c. the equilibrium position
d. revolution d. the restoring force
13. For a system in simple harmonic motion, which 17. A wave travels through a medium. As the wave
of the following is the number of cycles or passes, the particles of the medium vibrate in a
vibrations per unit of time? direction perpendicular to the direction of the
a. amplitude waves motion. The wave is
b. period a. longitudinal.
c. frequency b. a pulse.
d. revolution c. electromagnetic.
d. transverse.
14. How are frequency and period related in simple
harmonic motion? 18. Which of the following is a single nonperiodic
a. They are directly related. disturbance?
b. They are inversely related. a. pulse wave
c. Their sum is constant. b. periodic wave
d. Both measure the number of cycles per unit c. sine wave
of time. d. transverse wave
15. If a pendulum is adjusted so that its frequency 19. One end of a taut rope is fixed to a post. What
changes from 10 Hz to 20 Hz, its period will type of wave is produced if the free end is
change from n seconds to quickly raised and lowered one time?
a. n/4 seconds. a. pulse wave
b. n/2 seconds. b. periodic wave
c. 2n seconds. c. sine wave
d. 4n seconds. d. longitudinal wave

2
Name: ______________________ ID: A

20. Each compression in the waveform of the 24. When a mechanical waves amplitude is tripled,
longitudinal wave shown above corresponds to the energy the wave carries in a given time
what feature of the transverse wave below it? interval is increased by a factor of
a. wavelength a. 3.
b. crests b. 6.
c. troughs c. 9.
d. amplitude d. 18.

21. Each stretched region in the waveform of the 25. When a mechanical waves amplitude is reduced
longitudinal wave shown above corresponds to by half, the energy the wave carries in a given
what feature of the transverse wave below it? time interval is
a. wavelength a. doubled.
b. crests b. increased by a factor of 1.4.
c. troughs c. decreased to one-half.
d. amplitude d. decreased to one-fourth.

22. Which of the following most affects the 26. Two mechanical waves can occupy the same
wavelength of a mechanical wave moving space at the same time because waves
through a medium? Assume that the frequency a. are matter.
of the wave remains constant. b. are displacements of matter.
a. the nature of the medium c. do not cause interference patterns.
b. the amplitude d. cannot pass through one another.
c. the height of a crest
d. the energy carried by the wave 27. Two waves traveling in opposite directions on a
rope meet and undergo complete destructive
23. Suppose that two sound waves passing through interference. Which of the following best
the same medium have different wavelengths. describes the waves a moment after the waves
Which of the following is most likely to be the meet and coincide?
reason for the differing wavelengths? a. The waves no longer exist.
a. the nature of the medium b. The waves continue unchanged.
b. differences in amplitude c. The waves reflect and travel backward.
c. differences in frequency d. A single wave continues along the rope.
d. the type of wave

3
Name: ______________________ ID: A

28. When two mechanical waves coincide, the

amplitude of the resultant wave is always ____
the amplitudes of each wave alone.
a. greater than
b. less than
c. the sum of
d. the same as
32. Which of the following types of interference
29. Two mechanical waves that have positive will occur when the pulses in the figure above
displacements from the equilibrium position meet?
meet and coincide. What kind of interference a. no interference
occurs? b. constructive interference
a. constructive c. destructive interference
b. destructive d. total interference
c. complete destructive
d. none

30. Two mechanical waves meet and coincide. One

wave has a positive displacement from the
equilibrium position, and the other wave has a
negative displacement. What kind of
interference occurs?
a. constructive
b. destructive
c. complete constructive 33. Which of the following types of interference
d. none will occur when the pulses in the figure above
meet?
a. no interference
b. complete constructive interference
c. partial interference
d. complete destructive interference

34. Consider two identical wave pulses on a rope

31. Which of the following types of interference having a fixed end. Suppose the first pulse
will occur when the pulses in the figure above reaches the end of the rope, is reflected back,
meet? and then meets the second pulse. When the two
a. no interference pulses overlap exactly, what will be the
b. constructive interference amplitude of the resultant pulse?
c. destructive interference a. zero
d. total interference b. same as the original pulses
c. double the amplitude of the original pulses
d. half the amplitude of the original pulses

35. Waves arriving at a fixed boundary are

a. neither reflected nor inverted.
b. reflected but not inverted.
c. reflected and inverted.
d. inverted but not reflected.

36. Waves arriving at a free boundary are

a. neither reflected nor inverted.
b. reflected but not inverted.
c. reflected and inverted.
d. inverted but not reflected.

4
Name: ______________________ ID: A

37. A student sends a pulse traveling on a taut rope

with one end attached to a post. What will the
student observe?
a. The pulse will not be reflected if the rope is
free to slide up and down on the post.
b. The pulse will be reflected and inverted if the
rope is free to slide up and down on the post.
c. The pulse will be reflected and inverted if the 42. The standing wave shown in the diagram above
rope is fixed to the post. would be produced on a string of length L by a
d. The pulse will not be inverted if the rope is wave having wavelength
fixed to the post. a. 1/2 L.
b. L.
38. Standing waves are produced by periodic waves c. 2 L.
of d. 4 L.
a. any amplitude and wavelength traveling in
the same direction.
b. the same amplitude and wavelength traveling
in the same direction.
c. any amplitude and wavelength traveling in
opposite directions.
d. the same frequency, amplitude, and
wavelength traveling in opposite directions.
43. How many nodes and antinodes are shown in
39. A 2.0 m long stretched rope is fixed at both the standing wave above?
ends. Which wavelength would not produce a. two nodes and three antinodes
standing waves on this rope? b. one node and two antinodes
a. 2.0 m c. one-third node and one antinode
b. 3.0 m d. three nodes and two antinodes
c. 4.0 m
d. 6.0 m 44. A 3.0 m long stretched string is fixed at both
ends. If standing waves with a wavelength of
40. Which of the following wavelengths would two-thirds L are produced on this string, how
produce standing waves on a string many nodes will be formed?
approximately 3.5 m long? a. 0
a. 2.33 m b. 2
b. 2.85 m c. 3
c. 3.75 m d. 4
d. 4.55 m
45. What is the fewest number of nodes a standing
41. Which of the following wavelengths would not wave can have?
produce standing waves on a rope whose length a. 1
is 1 m? b. 2
a. 2/3 m c. 3
b. 1 m d. 4
c. 2 m
d. 2 1/4 m

5
Name: ______________________ ID: A

46. How many nodes and antinodes are shown in

the standing wave above?
a. four nodes and four antinodes
b. four nodes and three antinodes
c. four nodes and five antinodes
d. five nodes and four antinodes

48. In the diagram above, use the superposition

principle to find the resultant wave of waves Q
and R.
a. a
b. b
c. c
d. d

49. The time for one cycle of a periodic process is called

the

a. amplitude.
47. In the diagram above, use the superposition b. wavelength.
principle to find the resultant wave of waves X c. frequency.
and Y. d. period.
a. a
b. b 50. For a periodic process, the number of cycles per unit
c. c time is called the
d. d
a. amplitude.
b. wavelength.
c. frequency.
d. period.

51. For vibrational motion, the maximum displacement

from the equilibrium point is called the

a. amplitude.
b. wavelength.
c. frequency.
d. period.

6
Name: ______________________ ID: A

52. A mass on a spring undergoes SHM. When the mass 57. A mass is attached to a vertical spring and bobs up and
is at its maximum displacement from equilibrium, its down between points A and B. Where is the mass
instantaneous velocity located when its potential energy is a minimum?

a. is maximum. a. at either A or B
b. is less than maximum, but not zero. b. midway between A and B
c. is zero. c. one-fourth of the way between A and B
d. cannot be determined from the information given. d. none of the above

53. A mass on a spring undergoes SHM. When the mass 58. A mass is attached to a vertical spring and bobs up and
passes through the equilibrium position, its down between points A and B. Where is the mass
instantaneous velocity located when its potential energy is a maximum?

a. is maximum. a. at either A or B
b. is less than maximum, but not zero. b. midway between A and B
c. is zero. c. one-fourth of the way between A and B
d. cannot be determined from the information given. d. none of the above

54. A mass on a spring undergoes SHM. When the mass 59. In a wave, the maximum displacement of points of the
is at maximum displacement from equilibrium, its wave from equilibrium is called the wave's
instantaneous acceleration
a. speed.
a. is a maximum. b. frequency.
b. is less than maximum, but not zero. c. wavelength.
c. is zero. d. amplitude.
d. cannot be determined from the information given
60. The distance between successive crests on a wave is
55. called the wave's
A mass is attached to a vertical spring and bobs up
and down between points A and B. Where is the mass
a. speed.
located when its kinetic energy is a minimum?
b. frequency.
c. wavelength.
a. at either A or B
d. amplitude.
b. midway between A and B
c. one-fourth of the way between A and B 61. The number of crests of a wave passing a point per
d. none of the above unit time is called the wave's

56. A mass is attached to a vertical spring and bobs up a. speed.

and down between points A and B. Where is the mass b. frequency.
located when its kinetic energy is a maximum?
c. wavelength.
d. amplitude.
a. at either A or B
b. midway between A and B 62. For a wave, the frequency times the wavelength is the
c. one-fourth of the way between A and B wave's
d. none of the above
a. speed.
b. amplitude.
c. intensity.
d. power.

7
Name: ______________________ ID: A

63. The frequency of a wave increases. What happens to 68. A string of mass m and length L is under tension T.
the distance between successive crests if the speed The speed of a wave in the string is v. What will be
remains constant? the speed of a wave in the string if the tension is
increased to 2T?
a. It increases.
b. It remains the same. a. 0.5T
c. It decreases. b. 0.71T
d. It cannot be determined from the information given. c. 1.4T
d. 2T
64. A wave moves on a string with wavelength
and frequency f. A second wave on the same 69. A wave pulse traveling to the right along a thin cord
string has wavelength 2 and travels with the reaches a discontinuity where the rope becomes thicker
and heavier. What is the orientation of the reflected
same velocity. What is the frequency of the
and transmitted pulses?
second wave?

a. 0.5f a. Both are right side up.

b. f b. The reflected pulse returns right side up while the
transmitted pulse is inverted.
c. 2f
c. The reflected pulse returns inverted while the
d. It cannot be determined from the information given.
transmitted pulse is right side up.
65. Consider a traveling wave on a string of length L, d. Both are inverted.
mass M, and tension T. A standing wave is set up.
Which of the following is true? 70. Two wave pulses with equal positive amplitudes pass
each other on a string, one is traveling toward the right
and the other toward the left. At the point that they
a. The wave velocity depends on M, L, T.
occupy the same region of space at the same time
b. The wavelength of the wave is proportional to the
frequency. a. constructive interference occurs.
c. The particle velocity is equal to the wave velocity. b. destructive interference occurs.
d. The wavelength is proportional to T. c. a standing wave is produced.
66. A string of mass m and length L is under tension T. d. a traveling wave is produced.
The speed of a wave in the string is v. What will be
the speed of a wave in the string if the mass of the 71. Two wave pulses pass each other on a string. The one
traveling toward the right has a positive amplitude,
string is increased to 2m, with no change in length? while the one traveling toward the left has an equal
amplitude in the negative direction. At the point that
a. 0.5v they occupy the same region of space at the same time
b. 0.71v
c. 1.4v a. constructive interference occurs.
d. 2v b. destructive interference occurs.
c. a standing wave is produced.
67. A string of mass m and length L is under tension T.
d. a traveling wave is produced.
The speed of a wave in the string is v. What will be
the speed of a wave in the string if the length is 72. What is the spring constant of a spring that stretches
increased to 2L, with no change in mass? 2.00 cm when a mass of 0.600 kg is suspended from
it?
a. 0.5v
b. 0.71v a. 0.300 N/m
c. 1.4v b. 30.0 N/m
d. 2v c. 2.94 N/m
d. 294 N/m

8
Name: ______________________ ID: A

73. A mass is attached to a spring of spring constant 60 77. A mass vibrates back and forth from the free end of an
N/m along a horizontal, frictionless surface. The ideal spring of spring constant 20 N/m with an
spring is initially stretched by a force of 5.0 N on the amplitude of 0.30 m. What is the kinetic energy of
mass and let go. It takes the mass 0.50 s to go back this vibrating mass when it is 0.30 m from its
to its equilibrium position when it is oscillating. equilibrium position?
What is the amplitude?
a. zero
a. 0.030 m b. 0.90 J
b. 0.083 m c. 0.45 J
c. 0.30 m d. It is impossible to give an answer without knowing
d. 0.83 m the object's mass.

74. A mass is attached to a spring of spring constant 60 78. A pendulum makes 12 complete swings in 8.0 s. (a)
N/m along a horizontal, frictionless surface. The What are its frequency and period on Earth?
spring is initially stretched by a force of 5.0 N on the
mass and let go. It takes the mass 0.50 s to go back
to its equilibrium position when it is oscillating. a. 1.5 Hz, 0.67 s
What is the period of oscillation? b. 0.67 Hz, 1.5 s
c. 0.24 Hz, 4.2 s
a. 0.50 s d. 4.2 Hz, 0.24 s
b. 1.0 s
c. 1.5 s 79. A 3.00-kg pendulum is 28.84 m long. What is its
period on Earth?
d. 2.0 s

75. A mass is attached to a spring of spring constant 60 a. 10.78 s

N/m along a horizontal, frictionless surface. The b. 7.891 s
spring is initially stretched by a force of 5.0 N on the
mass and let go. It takes the mass 0.50 s to go back c. 4.897 s
to its equilibrium position when it is oscillating. d. 0.09278 s
What is the frequency of oscillation?
80. A pendulum has a period of 2.0 s on Earth. What is
its length?
a. 0.50 Hz
b. 1.0 Hz
a. 2.0 m
c. 1.5 Hz b. 1.0 m
d. 2.0 Hz c. 0.70 m
76. d. 0.50 m
A mass on a spring undergoes SHM. It goes through
81. The pendulum of a grandfather clock is 1.0 m long.
10 complete oscillations in 5.0 s. What is the period?
What is its period on the Earth?

a. 0.020 s
a. 1.0 s
b. 0.50 s
b. 2.0 s
c. 2.0 s
c. 4.0 s
d. 50 s
d. 8.0 s

9
Name: ______________________ ID: A

82. The pendulum of a grandfather clock is 1.0 m long. 85.

What is its period on the Moon where the acceleration
due to gravity is only 1.7 m/s2?

a. 1.2 s
b. 2.4 s
c. 4.8 s
d. 23 s

83. A simple pendulum consists of a 0.25-kg spherical

mass attached to a massless string. When the mass is
displaced slightly from its equilibrium position and
released, the pendulum swings back and forth with a
frequency of 2.0 Hz. What frequency would have
FIGURE 11-2
resulted if a 0.50-kg mass (same diameter sphere) had
Figure 11-2 is a "snapshot" of a wave at a given time.
been attached to the string instead? The frequency of the wave is 120 Hz. What is the
wavelength?
a. 1.0 Hz
b. 2.0 Hz
a. 0.05 m
c. 1.4 Hz
b. 0.10 m
d. none of the above
c. 0.20 m
d. 0.30 m

84.
FIGURE 11-2
Figure 11-2 is a "snapshot" of a wave at a given time. 86.
The frequency of the wave is 120 Hz. What is the FIGURE 11-2
Figure 11-2 is a "snapshot" of a wave at a given time.
amplitude?
The frequency of the wave is 120 Hz. What is the
wave speed?
a. 0.05 m
b. 0.10 m
a. 12 m/s
c. 0.15 m
b. 24 m/s
d. 0.20 m
c. 36 m/s
d. 48 m/s

10
Name: ______________________ ID: A

87. What is the frequency of a wave which has a period of 88. What is the period of a wave with a frequency of 1500
6.00 ms? Hz?

a. 16.7 Hz a. 0.67 s
b. 167 Hz b. 0.67 ms
c. 1.67 kHz c. 0.67 s
d. 16.7 kHz d. 6.7 s

Problem

89. If a force of 52 N stretches a spring 0.36 m, 97. A truck with bad shock absorbers bounces up
what is the spring constant? and down after hitting a bump. The truck has a
mass of 1700 kg and is supported by four
90. A 0.35 kg mass suspended from a spring moves springs, each having a spring constant of 6200
with simple harmonic motion. At the instant N/m. What is the period for each spring?
the mass is displaced from equilibrium by
0.105 m, what is its acceleration? (The spring 98. What is the period of a 6.93 m long pendulum
constant is 11.8 N/m.) with a bob of mass 68.0 kg? Assume the
2
acceleration due to gravity is 9.81 m/s .
91. How much displacement will a coil spring with a
spring constant of 110 N/m achieve if it is 99. On the planet Xenos, an astronaut observes
stretched by a 70 N force? that a 1.88 m long pendulum has a period of
1.85 s. What is the free-fall acceleration on
92. A mass on a spring that has been compressed Xenos?
0.29 m has a restoring force of 82 N. What is
the spring constant? 100. A student wishes to construct a mass-spring
system that will oscillate with the same
93. An amusement park ride has a frequency of frequency as a swinging pendulum with a period
0.064 Hz. What is the rides period? of 3.99 s. The student has a spring with a spring
constant of 77.1 N/m. What mass should the
94. Imagine that you could transport a simple student use to construct the mass-spring
pendulum from Earth to another planet or system?
moon, where the free-fall acceleration is
one-fifth that on Earth. By what factor would 101. A periodic wave has a wavelength of 0.58 m
the pendulums frequency be changed? Express and a speed of 14 m/s. What is the wave
the answer with one significant figure. frequency?

95. An amusement park ride swings back and forth 102. A musical tone sounded on a piano has a
once every 17.4 s. What is the rides frequency of 215.1 Hz and a wavelength of
frequency? 1.47 m. What is the speed of the sound wave?

96. A mass on a spring vibrates in simple harmonic 103. Radio waves from an FM station have a
motion at an amplitude of 8.0 cm. If the mass frequency of 95.9 MHz. If the waves travel
of the object is 0.65 kg and the spring constant 8
with a speed of 3.00 10 m/s, what is the
is 120 N/m, what is the frequency?
wavelength?

11
Name: ______________________ ID: A

104. Bats chirp at high frequencies that humans

cannot hear. They use the echoes to detect
objects, such as insects, that are as small as one
wavelength. If a bat emits a chirp at a
frequency of 45.4 kHz and the speed of sound
waves in air is 340 m/s, what is the size in
millimeters of the smallest insect that the bat
can detect?

105. Waves propagate along a stretched string at a

speed of 6.9 m/s. The end of the string vibrates
up and down once every 3.6 s. What is the
wavelength of the waves traveling along the
string?

106. Vibration of a certain frequency produces a

standing wave on a stretched string that is 1.6
m long. The standing wave has 7 nodes and 5
antinodes. What is the wavelength of the wave
that produces this standing wave?

12
 ID: A

11th Grade Midterm Workbook

Answer Section

MULTIPLE CHOICE

1. ANS: A PTS: 1 DIF: I OBJ: 11-1.1

2. ANS: B PTS: 1 DIF: II OBJ: 11-1.1
3. ANS: C PTS: 1 DIF: II OBJ: 11-1.2
4. ANS: B PTS: 1 DIF: I OBJ: 11-1.2
5. ANS: C PTS: 1 DIF: I OBJ: 11-1.2
6. ANS: A PTS: 1 DIF: I OBJ: 11-1.2
7. ANS: D PTS: 1 DIF: II OBJ: 11-1.2
8. ANS: D PTS: 1 DIF: I OBJ: 11-2.1
9. ANS: A PTS: 1 DIF: I OBJ: 11-2.1
10. ANS: B PTS: 1 DIF: II OBJ: 11-2.1
11. ANS: B PTS: 1 DIF: II OBJ: 11-2.1
12. ANS: B PTS: 1 DIF: I OBJ: 11-2.2
13. ANS: C PTS: 1 DIF: I OBJ: 11-2.2
14. ANS: B PTS: 1 DIF: I OBJ: 11-2.2
15. ANS: B PTS: 1 DIF: II OBJ: 11-2.2
16. ANS: D PTS: 1 DIF: IIIA OBJ: 11-2.3
17. ANS: D PTS: 1 DIF: I OBJ: 11-3.1
18. ANS: A PTS: 1 DIF: I OBJ: 11-3.2
19. ANS: A PTS: 1 DIF: I OBJ: 11-3.2
20. ANS: B PTS: 1 DIF: I OBJ: 11-3.3
21. ANS: C PTS: 1 DIF: I OBJ: 11-3.3
22. ANS: A PTS: 1 DIF: II OBJ: 11-3.4
23. ANS: C PTS: 1 DIF: II OBJ: 11-3.4
24. ANS: C PTS: 1 DIF: I OBJ: 11-3.5
25. ANS: D PTS: 1 DIF: II OBJ: 11-3.5
26. ANS: B PTS: 1 DIF: I OBJ: 11-4.1
27. ANS: B PTS: 1 DIF: II OBJ: 11-4.1
28. ANS: C PTS: 1 DIF: I OBJ: 11-4.2
29. ANS: A PTS: 1 DIF: I OBJ: 11-4.2
30. ANS: B PTS: 1 DIF: I OBJ: 11-4.2
31. ANS: B PTS: 1 DIF: I OBJ: 11-4.2
32. ANS: C PTS: 1 DIF: I OBJ: 11-4.2
33. ANS: D PTS: 1 DIF: I OBJ: 11-4.2
34. ANS: A PTS: 1 DIF: IIIA OBJ: 11-4.3
35. ANS: C PTS: 1 DIF: I OBJ: 11-4.3
36. ANS: B PTS: 1 DIF: I OBJ: 11-4.3
37. ANS: C PTS: 1 DIF: II OBJ: 11-4.3
38. ANS: D PTS: 1 DIF: I OBJ: 11-4.4
39. ANS: B PTS: 1 DIF: IIIA OBJ: 11-4.4
40. ANS: A PTS: 1 DIF: IIIC OBJ: 11-4.4
41. ANS: D PTS: 1 DIF: I OBJ: 11-4.4
42. ANS: B PTS: 1 DIF: II OBJ: 11-4.4
43. ANS: D PTS: 1 DIF: I OBJ: 11-4.5
44. ANS: D PTS: 1 DIF: II OBJ: 11-4.5

1
 ID: A

45. ANS: B PTS: 1 DIF: I OBJ: 11-4.5

46. ANS: D PTS: 1 DIF: I OBJ: 11-4.5
47. ANS: A PTS: 1 DIF: II OBJ: 11-4.1
48. ANS: B PTS: 1 DIF: II OBJ: 11-4.1
49. ANS: D PTS: 1 DIF: 1
REF: SHM, Energy in SHM, Period and Sinusoidal Nature of SHM
50. ANS: C PTS: 1 DIF: 1
REF: SHM, Energy in SHM, Period and Sinusoidal Nature of SHM
51. ANS: A PTS: 1 DIF: 1
REF: SHM, Energy in SHM, Period and Sinusoidal Nature of SHM
52. ANS: C PTS: 1 DIF: 1
REF: SHM, Energy in SHM, Period and Sinusoidal Nature of SHM
53. ANS: A PTS: 1 DIF: 1
REF: SHM, Energy in SHM, Period and Sinusoidal Nature of SHM
54. ANS: A PTS: 1 DIF: 1
REF: SHM, Energy in SHM, Period and Sinusoidal Nature of SHM
55. ANS: A PTS: 1 DIF: 2
REF: SHM, Energy in SHM, Period and Sinusoidal Nature of SHM
56. ANS: B PTS: 1 DIF: 2
REF: SHM, Energy in SHM, Period and Sinusoidal Nature of SHM
57. ANS: B PTS: 1 DIF: 2
REF: SHM, Energy in SHM, Period and Sinusoidal Nature of SHM
58. ANS: A PTS: 1 DIF: 2
REF: SHM, Energy in SHM, Period and Sinusoidal Nature of SHM
59. ANS: D PTS: 1 DIF: 1
REF: Wave Motion, Types of Waves; Transverse and Longitudinal
60. ANS: C PTS: 1 DIF: 1
REF: Wave Motion, Types of Waves; Transverse and Longitudinal
61. ANS: B PTS: 1 DIF: 1
REF: Wave Motion, Types of Waves; Transverse and Longitudinal
62. ANS: A PTS: 1 DIF: 1
REF: Wave Motion, Types of Waves; Transverse and Longitudinal
63. ANS: C PTS: 1 DIF: 1
REF: Wave Motion, Types of Waves; Transverse and Longitudinal
64. ANS: A PTS: 1 DIF: 1
REF: Wave Motion, Types of Waves; Transverse and Longitudinal
65. ANS: A PTS: 1 DIF: 2
REF: Wave Motion, Types of Waves; Transverse and Longitudinal
66. ANS: B PTS: 1 DIF: 1
REF: Wave Motion, Types of Waves; Transverse and Longitudinal
67. ANS: C PTS: 1 DIF: 1
REF: Wave Motion, Types of Waves; Transverse and Longitudinal
68. ANS: C PTS: 1 DIF: 2
REF: Wave Motion, Types of Waves; Transverse and Longitudinal
69. ANS: C PTS: 1 DIF: 1 REF: Reflection and Transmissionof
Waves
70. ANS: A PTS: 1 DIF: 1
REF: Interference ; Principle of Superposition
71. ANS: B PTS: 1 DIF: 1
REF: Interference ; Principle of Superposition

2
 ID: A

72. ANS: D PTS: 1 DIF: 1

REF: Reflection and Transmission of Waves, Interference; Principle of Superpisition, Standing Waves :
Resonance NOT: Q
73. ANS: B PTS: 1 DIF: 1
REF: Reflection and Transmission of Waves, Interference; Principle of Superpisition, Standing Waves :
Resonance NOT: Q
74. ANS: D PTS: 1 DIF: 1
REF: Reflection and Transmission of Waves, Interference; Principle of Superpisition, Standing Waves :
Resonance NOT: Q
75. ANS: A PTS: 1 DIF: 1
REF: Reflection and Transmission of Waves, Interference; Principle of Superpisition, Standing Waves :
Resonance NOT: Q
76. ANS: B PTS: 1 DIF: 1
REF: Reflection and Transmission of Waves, Interference; Principle of Superpisition, Standing Waves :
Resonance NOT: Q
77. ANS: A PTS: 1 DIF: 1
REF: Reflection and Transmission of Waves, Interference; Principle of Superpisition, Standing Waves :
Resonance NOT: Q
78. ANS: A PTS: 1 DIF: 1 REF: Refraction
NOT: Q
79. ANS: A PTS: 1 DIF: 1 REF: Refraction
NOT: Q
80. ANS: B PTS: 1 DIF: 1 REF: Refraction
NOT: Q
81. ANS: B PTS: 1 DIF: 1 REF: Refraction
NOT: Q
82. ANS: C PTS: 1 DIF: 1 REF: Refraction
NOT: Q
83. ANS: B PTS: 1 DIF: 1 REF: Refraction
NOT: Q
84. ANS: B PTS: 1 DIF: 1
REF: Wave Motion, Types of Waves: Transverse and Longitudinal
NOT: Q
85. ANS: C PTS: 1 DIF: 1
REF: Wave Motion, Types of Waves: Transverse and Longitudinal
NOT: Q
86. ANS: B PTS: 1 DIF: 1
REF: Wave Motion, Types of Waves: Transverse and Longitudinal
NOT: Q
87. ANS: B PTS: 1 DIF: 1
REF: Wave Motion, Types of Waves: Transverse and Longitudinal
NOT: Q
88. ANS: B PTS: 1 DIF: 1
REF: Wave Motion, Types of Waves: Transverse and Longitudinal
NOT: Q

3
 ID: A

PROBLEM

89. ANS:
140 N/m

Given
F elastic = 52 N
x = 0.36 m

Solution
F elastic = kx
F elastic 52 N
k= =
x 0.36 m
k = 140 N/m

PTS: 1 DIF: IIIA OBJ: 11-1.3

90. ANS:
2
3.5 m/s

Given
m = 0.35 kg
k = 11.8 N/m
x = 0.105 m

Solution
F = kx and F = ma
m a = kx
kx (11.8 N/m)(0.105 m)
a= =
m 0.35 kg
2
a = 3.5 N/kg = 3.5 m/s

PTS: 1 DIF: IIIA OBJ: 11-1.3

91. ANS:
0.6 m

Given
k = 110 N/m
F elastic = 70 N

Solution
F elastic = kx
F elastic 70 N
x= =
k 110 N/m
x = 0.6 m

PTS: 1 DIF: IIIA OBJ: 11-1.3

4
 ID: A

92. ANS:
280 N/m

Given
x = 0.29 m
F elastic = 82 N

Solution
F elastic = kx
F elastic82 N
k= =
x 0.29 m
k = 280 N/m

PTS: 1 DIF: IIIB OBJ: 11-1.3

93. ANS:
16 s

Given
f = 0.064 Hz

Solution
1 1
T= =
f 0.064 Hz

T = 16 s

PTS: 1 DIF: IIIA OBJ: 11-2.3

5
 ID: A

94. ANS:
0.4

Given
1
ag = g
5

Solution
L
T = 2
ag

Because L and 2 remain constant when the pendulum is relocated,

1
T new ,
ag

where a g is the gravitational acceleration of the planet or moon.

1
T new ag
g
= =
T Earth 1 ag
g

f new T Earth ag
1 1
f = , so = = = = 0.4
T f Earth T new g 5

PTS: 1 DIF: IIIB OBJ: 11-2.3

95. ANS:
2
5.75 10 Hz

Given
T = 17.4 s

Solution
1 1 2
f= = = 5.75 10 Hz
T 17.4

PTS: 1 DIF: IIIA OBJ: 11-2.3

6
 ID: A

96. ANS:
2.1 Hz

Given
x = 8.0 cm
m = 0.65 kg
k = 120 N/m

Solution

m 1
T = 2 and f = , so
k T

1 1 k
f= =
m 2 m
2
k

1 120 N/m
f= = 2.1 Hz
2 0.65 kg

PTS: 1 DIF: IIIB OBJ: 11-2.3

97. ANS:
1.6 s

Given
m total = 1700 kg
k(per spring) = 6200 N/m

Solution
Assume that the total mass of 1700 kg is supported equally on the four springs. Each spring then supports
1700/4 kg.

m (1700 / 4) kg
T = 2 = 2 = 1.6 s
k 6200 N/m

PTS: 1 DIF: IIIB OBJ: 11-2.3

7
 ID: A

98. ANS:
5.28 s

Given
L = 6.93 m
m = 68.0 kg
2
g = 9.81 m/s

Solution
L 6.93 m
T = 2 = 2 = 5.28 s
ag 9.81 m/s
2

PTS: 1 DIF: IIIB OBJ: 11-2.3

99. ANS:
2
21.7 m/s

Given
L = 1.88 m
T = 1.85 s

Solution

L 2
L
T = 2
2
, so T = 4

ag a g


1.88 m
2
4 L 2 2
ag = 2
= 4
2 = 21.7 m/s
T ( 1.85 s)

PTS: 1 DIF: IIIB OBJ: 11-2.3

8
 ID: A

100. ANS:
31.1 kg

Given
T pendulum = 3.99 s

k = 77.1 N/m

Solution
If both systems have the same frequency, they will also have the same period.
Therefore, the given period may be substituted into the equation for a mass-spring system.
m
T = 2
k

2m

T = 4
2

k

2 2
T k ( 3.99 s) ( 77.1 N/m )
m= 2
= 2
= 31.1 kg
4 4

PTS: 1 DIF: IIIC OBJ: 11-2.3

101. ANS:
24 Hz

Given
v = 0.58 m/s
= 14 m

Solution
v = f
v 14 m/s
f= = = 24 Hz
0.58 m

PTS: 1 DIF: IIIA OBJ: 11-3.4

102. ANS:
316 m/s

Given
f = 215.1 Hz
= 1.47 m

Solution
v = f
v = (215.1 Hz)(1.47 m) = 316 m/s

PTS: 1 DIF: IIIA OBJ: 11-3.4

9
 ID: A

103. ANS:
3.13 m

Given
8
f = 95.9 MHz = 0.959 10 Hz
8
v = 3.00 10 m/s

Solution
v = f
8
v 3.00 10 m/s
= = = 3.13 m
f 8
0.959 10 Hz

PTS: 1 DIF: IIIA OBJ: 11-3.4

104. ANS:
7.5 mm

Given
f = 45.4 kHz
v = 340 m/s

Solution
v = f
4
f = 45.4 kHz = 4.54 10 Hz
v 340 m/s
= = = 0.0075 m = 7.5 mm
f 4
4.54 10 Hz

PTS: 1 DIF: IIIB OBJ: 11-3.4

105. ANS:
25 m

Given
v = 6.9 m/s
T = 3.6 s

Solution
1 1
f= = = 0.28 Hz
T 3.6 s
v = f
v 6.9 m/s
= = = 25 m
f 0.28 Hz

PTS: 1 DIF: IIIB OBJ: 11-3.4

10
 ID: A

106. ANS:
0.64 m

Given
L = 1.6 m
The standing wave has 5 antinodes, i.e., 5 loops.

Solution
A single loop (antinode) is produced by a wavelength equal to 2L. Two loops (one complete wavelength)
are produced by a wavelength of L. A wavelength of 2/3 L results in 3 antinodes. The following pattern
emerges.

1 loop = 2L/1 = 2L
2 loops = 2L/2 = L
3 loops = 2L/3 = 2/3 L
4 loops = 2L/4 = 1/2 L
5 loops = 2L/5 = 2/5 L

therefore,

2 2(1.6 m)
= L = = 0.64 m
5 5

PTS: 1 DIF: IIIC OBJ: 11-4.5

11