Question 1

What are the first three harmonics of a string of linear mass density 2.00 g/m and length 0.600 m when it is subjected to tension of 50.0 N?

Accepted Answer

132. Hz, 264. Hz, 396. Hz

Question 2

The condition of driving a system at a natural frequency is referred to as resonance.

Accepted Answer

A) True 
 B)False  True

Question 3

When the length of a simple pendulum is tripled, the time for one complete vibration increases by a factor of

Accepted Answer

A)  1/3. 
B)   
C)  9. 
D)  3. 
E)  1/9. 
A)  1/3. 
B)   
C)  9. 
D)  3. 
E)  1/9. B

Question 4

The lower the frequency of a sound wave, the

Accepted Answer

A)  shorter its period. 
B)  lower its velocity. 
C)  greater its velocity. 
D)  greater its wavelength. 
E)  smaller its amplitude. 
A)  shorter its period. 
B)  lower its velocity. 
C)  greater its velocity. 
D)  greater its wavelength. 
E)  smaller its amplitude.

Question 5

Simple pendulum A swings back and forth at twice the frequency of simple pendulum B. Which statement is correct?

Accepted Answer

A)  Amplitude of B is twice of A. 
B)  Amplitude of pendulum A is twice that of B. 
C)  Amplitude of A is 1.41 that of B. 
D)  Amplitude can not be determined from data given. 
A)  Amplitude of B is twice of A. 
B)  Amplitude of pendulum A is twice that of B. 
C)  Amplitude of A is 1.41 that of B. 
D)  Amplitude can not be determined from data given.

Question 6

A mass is attached to a vertical spring and bobs up and down between points A and B. Where is the mass located when its kinetic energy is a maximum?

Accepted Answer

A)  at either A or B 
B)  one-fourth of the way between A and B 
C)  midway between A and B 
A)  at either A or B 
B)  one-fourth of the way between A and B 
C)  midway between A and B

Question 7

Find the first three harmonics of a string of linear mass density 2.00 g/m and length 0.600 m when it is subjected to tension of 50.0 N.

Accepted Answer

A)  264 Hz, 528 Hz, 792 Hz 
B)  66 Hz, 132 Hz, 198 Hz 
C)  132 Hz, 264 Hz, 396 Hz 
D)  none of the above 
A)  264 Hz, 528 Hz, 792 Hz 
B)  66 Hz, 132 Hz, 198 Hz 
C)  132 Hz, 264 Hz, 396 Hz 
D)  none of the above

Question 8

What is the frequency (in Hz) of a wave whose displacement is given y = 50. sin(0.20x + 120t), where x and y are in cm and t in seconds?

Accepted Answer

A)  0.5 Hz 
B)  19. Hz 
C)  0.120 kHz 
D)  120   Hz 
E)  10 Hz 
A)  0.5 Hz 
B)  19. Hz 
C)  0.120 kHz 
D)  120   Hz 
E)  10 Hz

Question 9

A long rope of linear density 0.25 kg/m is under tension. Transverse waves travel on it at 30. m/s. How much energy is stored in 1.0 m of the rope when a driving frequency of 6.0 Hz produces a traveling wave with an amplitude of 0.10 m?

Accepted Answer

The answer of A long rope of linear density 0.25...

Question 10

An object oscillates such that its displacement is x = (0.222 m) sin(314.t) where t is in seconds.
(a) In one period, the object moves what distance?
(b) What is the frequency?
(c) What is the position at t = 1.00 s?

Accepted Answer

(a) 0.888

Question 11

A string, fixed at both ends, vibrates at a frequency of 12 Hz with a standing transverse wave pattern containing 3 loops. What frequency is needed if the standing wave pattern is to contain 4 loops?

Accepted Answer

A)  48 Hz 
B)  16 Hz 
C)  36 Hz 
D)  18 Hz 
E)  12 Hz 
A)  48 Hz 
B)  16 Hz 
C)  36 Hz 
D)  18 Hz 
E)  12 Hz

Question 12

A mass attached to the free end of an ideal spring executes SHM according to the equation x = 0.50 sin(18.t) where x is in meters and t is in seconds. What is the maximum velocity of the mass?

Accepted Answer

A)  36 m/s 
B)  3   m/s 
C)  3 m/s 
D)  9 m/s 
E)  3   m/s 
A)  36 m/s 
B)  3   m/s 
C)  3 m/s 
D)  9 m/s 
E)  3   m/s

Question 13

Waves on a lake pass under a floating bird causing the bird to bob up and down with a period of 2.5 seconds. If the distance from wave trough to wave trough is 3.0 meters, what is the speed of the wave?

Accepted Answer

A)  1.5 m/s 
B)  2.1 m/s 
C)  1.2 m/s 
D)  1.9 m/s 
E)  0.21 m/s 
A)  1.5 m/s 
B)  2.1 m/s 
C)  1.2 m/s 
D)  1.9 m/s 
E)  0.21 m/s

Question 14

Does Simple Harmonic Motion occur when the force, acting on a mass, is positively proportional to the displacement (F = kx)? Explain.

Accepted Answer

No. F = kx (k positive) leads

Question 15

A mountain climber of mass 60. kg slips and falls a distance of 4.0 m, at which time he reaches the end of his elastic safety rope. The rope then stretches an additional 2.0 m before the climber comes to rest. What is the spring constant of the rope, assuming it obeys Hooke's law?

Accepted Answer

The answer of A mountain climber of mass 60. kg...

Question 16

A mass attached to the free end of an ideal spring executes SHM according to the equation x = 0.5 sin(20 t) where x is in meters and t is in seconds. What is the magnitude of the maximum acceleration for this mass?

Accepted Answer

A)  200 m/s2 
B)  10 m/s2 
C)  100 m/s2 
D)  20 m/s2 
E)  (20/ $\pi$) m/s2 
A)  200 m/s2 
B)  10 m/s2 
C)  100 m/s2 
D)  20 m/s2 
E)  (20/ $\pi$) m/s2

Question 17

A string of linear density 6.00 g/m is under a tension of 180. N. What is the velocity of propagation of transverse waves along the string?

Accepted Answer

The answer of A string of linear density 6.00 g/m...

Question 18

A stretched string is observed to have three equal segments in a standing wave driven at a frequency of 480. Hz. What driving frequency will set up a standing wave with four equal segments?

Accepted Answer

The answer of A stretched string is observed to have...

Question 19

Consider the wave shown in Figure 13-4
  
 The amplitude is

Accepted Answer

A)  4 m. 
B)  8 m. 
C)  2 m. 
D)  cannot be determined from given information 
A)  4 m. 
B)  8 m. 
C)  2 m. 
D)  cannot be determined from given information

Question 20

What happens to a simple pendulum's frequency if both its length and mass are increased?

Accepted Answer

A)  It increases. 
B)  It decreases. 
C)  It remains constant. 
D)  It could remain constant, increase, or decrease; it depends on the mass to length ratio (mass density). 
A)  It increases. 
B)  It decreases. 
C)  It remains constant. 
D)  It could remain constant, increase, or decrease; it depends on the mass to length ratio (mass density).

Exam 13: Vibrations and Waves

What are the first three harmonics of a string of linear mass density 2.00 g/m and length 0.600 m when it is subjected to tension of 50.0 N?

The condition of driving a system at a natural frequency is referred to as resonance.

When the length of a simple pendulum is tripled, the time for one complete vibration increases by a factor of

The lower the frequency of a sound wave, the

Simple pendulum A swings back and forth at twice the frequency of simple pendulum B. Which statement is correct?

A mass is attached to a vertical spring and bobs up and down between points A and B. Where is the mass located when its kinetic energy is a maximum?

Find the first three harmonics of a string of linear mass density 2.00 g/m and length 0.600 m when it is subjected to tension of 50.0 N.

What is the frequency (in Hz) of a wave whose displacement is given y = 50. sin(0.20x + 120t), where x and y are in cm and t in seconds?

A long rope of linear density 0.25 kg/m is under tension. Transverse waves travel on it at 30. m/s. How much energy is stored in 1.0 m of the rope when a driving frequency of 6.0 Hz produces a traveling wave with an amplitude of 0.10 m?

An object oscillates such that its displacement is x = (0.222 m) sin(314.t) where t is in seconds. (a) In one period, the object moves what distance? (b) What is the frequency? (c) What is the position at t = 1.00 s?

A string, fixed at both ends, vibrates at a frequency of 12 Hz with a standing transverse wave pattern containing 3 loops. What frequency is needed if the standing wave pattern is to contain 4 loops?

A mass attached to the free end of an ideal spring executes SHM according to the equation x = 0.50 sin(18.t) where x is in meters and t is in seconds. What is the maximum velocity of the mass?

Waves on a lake pass under a floating bird causing the bird to bob up and down with a period of 2.5 seconds. If the distance from wave trough to wave trough is 3.0 meters, what is the speed of the wave?

Does Simple Harmonic Motion occur when the force, acting on a mass, is positively proportional to the displacement (F = kx)? Explain.

A mountain climber of mass 60. kg slips and falls a distance of 4.0 m, at which time he reaches the end of his elastic safety rope. The rope then stretches an additional 2.0 m before the climber comes to rest. What is the spring constant of the rope, assuming it obeys Hooke's law?

A mass attached to the free end of an ideal spring executes SHM according to the equation x = 0.5 sin(20 t) where x is in meters and t is in seconds. What is the magnitude of the maximum acceleration for this mass?

A string of linear density 6.00 g/m is under a tension of 180. N. What is the velocity of propagation of transverse waves along the string?

A stretched string is observed to have three equal segments in a standing wave driven at a frequency of 480. Hz. What driving frequency will set up a standing wave with four equal segments?

Consider the wave shown in Figure 13-4 The amplitude is

What happens to a simple pendulum's frequency if both its length and mass are increased?

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