Question 1

In the figure, which of the curves best represents the variation of wave speed as a function of tension for transverse waves on a stretched string?

Accepted Answer

A)  A 
B)  B 
C)  C 
D)  D 
E)  E 
A)  A 
B)  B 
C)  C 
D)  D 
E)  E

Question 2

A 6.0-m wire with a mass of 50 g, is under tension. A transverse wave, for which the frequency is 810 Hz, the wavelength is 0.40 m, and the amplitude is 4.0 mm, is propagating on the wire. The time for a crest of this wave to travel the length of the wire is closest to

Accepted Answer

A)  19 ms. 
B)  16 ms. 
C)  21 ms. 
D)  23 ms. 
E)  25 ms. 
A)  19 ms. 
B)  16 ms. 
C)  21 ms. 
D)  23 ms. 
E)  25 ms.

Question 3

A 2.0-m string is fixed at both ends and tightened until the wave speed is 78m/s. What is the frequency of the standing wave shown in the figure?

Accepted Answer

A)  120 Hz 
B)  230 Hz 
C)  350 Hz 
D)  470 Hz 
A)  120 Hz 
B)  230 Hz 
C)  350 Hz 
D)  470 Hz

Question 4

When a weight W is hanging from a light vertical string, the speed of pulses on the string is V. If a second weight W is added without stretching the string, the speed of pulses on this string will now become

Accepted Answer

A)  2V. 
B)    V. 
C)  V. 
D)  V/   . 
E)  V/2 
A)  2V. 
B)    V. 
C)  V. 
D)  V/   . 
E)  V/2

Question 5

The vertical displacement y(x,t) of a string stretched along the horizontal x-axis is given by y(x,t) = (6.00 mm) cos[(3.25 m-1)x - (7.22 rad/s)t].
(a) What is the minimum time for each complete cycle of the wave?
(b) What is the distance between adjacent crests of the wave?
(c) How fast does this wave travel?

Accepted Answer

(a) 0.870

Question 6

A 6.00-m long rope is under a tension of 600 N. Waves travel along this rope at 40.0 m/s. What is the mass of the rope?

Accepted Answer

A)  1.00 kg 
B)  1.25 kg 
C)  2.25 kg 
D)  2.50 kg 
E)  1.12 kg 
A)  1.00 kg 
B)  1.25 kg 
C)  2.25 kg 
D)  2.50 kg 
E)  1.12 kg

Question 7

Standing waves of frequency 57 Hz are produced on a string that has mass per unit length 0.0160 kg/m. With what tension must the string be stretched between two supports if adjacent nodes in the standing wave are to be 0.71 meters apart?

Accepted Answer

The answer of Standing waves of frequency 57 Hz are...

Question 8

For the wave shown in the figure, the frequency is

Accepted Answer

A)  0.5 Hz. 
B)  1 Hz. 
C)  2 Hz. 
D)  4 Hz. 
E)  unable to be determined from the given information. 
A)  0.5 Hz. 
B)  1 Hz. 
C)  2 Hz. 
D)  4 Hz. 
E)  unable to be determined from the given information.

Question 9

A standing wave is oscillating at 690 Hz on a string, as shown in the figure. What is the speed of traveling waves on this string?

Accepted Answer

A)  280 m/s 
B)  410 m/s 
C)  210 m/s 
D)  140 m/s 
A)  280 m/s 
B)  410 m/s 
C)  210 m/s 
D)  140 m/s

Question 10

A thin 2.00-m string of mass 50.0 g is fixed at both ends and under a tension of 70.0 N. If it is set into small-amplitude oscillation, what is the frequency of the first harmonic mode?

Accepted Answer

A)  6.61 Hz 
B)  13.2 Hz 
C)  26.5 Hz 
D)  52.9 Hz 
A)  6.61 Hz 
B)  13.2 Hz 
C)  26.5 Hz 
D)  52.9 Hz

Question 11

A heavy stone of mass m is hung from the ceiling by a thin 8.25-g wire that is 65.0 cm long. When you gently pluck the upper end of the wire, a pulse travels down the wire and returns 7.84 ms later, having reflected off the lower end. The speed of sound in the room is 344 m/s, and the stone is heavy enough to prevent the lower end of the wire from moving. If the wire is vibrating in its second overtone, what is the frequency of the sound it will produce?

Accepted Answer

A)  128 Hz 
B)  191 Hz 
C)  255 Hz 
D)  383 Hz 
E)  765 Hz 
A)  128 Hz 
B)  191 Hz 
C)  255 Hz 
D)  383 Hz 
E)  765 Hz

Question 12

A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thinner and lighter. What is the orientation of the reflected and transmitted pulses?

Accepted Answer

A)  Both pulses are right side up. 
B)  The reflected pulse returns right side up while the transmitted pulse is inverted. 
C)  The reflected pulse returns inverted while the transmitted pulse is right side up. 
D)  Both pulses are inverted. 
A)  Both pulses are right side up. 
B)  The reflected pulse returns right side up while the transmitted pulse is inverted. 
C)  The reflected pulse returns inverted while the transmitted pulse is right side up. 
D)  Both pulses are inverted.

Question 13

Consider the waves on a vibrating guitar string and the sound waves the guitar produces in the surrounding air. The string waves and the sound waves must have the same

Accepted Answer

A)  wavelength. 
B)  velocity. 
C)  frequency. 
D)  amplitude. 
E)  More than one of the above is true. 
A)  wavelength. 
B)  velocity. 
C)  frequency. 
D)  amplitude. 
E)  More than one of the above is true.

Question 14

You and your surfing buddy are waiting to catch a wave a few hundred meters off the beach. The waves are conveniently sinusoidal, and you notice that when you're on the top of one wave and moving toward your friend, she is exactly halfway between you and the trough of the wave. 1.50 seconds later, your friend is at the top of the wave. You estimate the horizontal distance between you and your friend at 8.00 m.
(a) What is the frequency of the waves?
(b) Find the speed of the waves.

Accepted Answer

(a) 0.167

Question 15

A transverse wave is traveling on a string stretched along the horizontal x-axis. The equation for the vertical displacement y of the string is given by y = 0.0020 cos[π(15x - 52t)], where all quantities are in SI units. The maximum speed of a particle of the string is closest to

Accepted Answer

A)  0.33 m/s. 
B)  0.43 m/s. 
C)  0.53 m/s. 
D)  0.64 m/s. 
E)  0.74 m/s. 
A)  0.33 m/s. 
B)  0.43 m/s. 
C)  0.53 m/s. 
D)  0.64 m/s. 
E)  0.74 m/s.

Question 16

The figure shows the displacement y of a traveling wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. How fast is the wave traveling?

Accepted Answer

A)  3.0 m/s 
B)  0.75 m/s 
C)  0.66 m/s 
D)  1.5 m/s 
E)  2.0 m/s 
A)  3.0 m/s 
B)  0.75 m/s 
C)  0.66 m/s 
D)  1.5 m/s 
E)  2.0 m/s

Question 17

The figure shows the displacement y of a wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. Determine the frequency of the wave.

Accepted Answer

A)  4.0 Hz 
B)  0.50 Hz 
C)  3.0 Hz 
D)  0.33 Hz 
E)  0.25 Hz 
A)  4.0 Hz 
B)  0.50 Hz 
C)  3.0 Hz 
D)  0.33 Hz 
E)  0.25 Hz

Question 18

A 8.0-m long wire with a mass of 10 g is under tension. A transverse wave for which the frequency is 570 Hz, the wavelength is 0.10 m, and the amplitude is 3.7 mm is propagating on the wire. The maximum transverse acceleration of a point on a wire is closest to

Accepted Answer

A)  47,000 m/s2. 
B)  41,000 m/s2. 
C)  35,000 m/s2. 
D)  29,000 m/s2. 
E)  53,000 m/s2. 
A)  47,000 m/s2. 
B)  41,000 m/s2. 
C)  35,000 m/s2. 
D)  29,000 m/s2. 
E)  53,000 m/s2.

Question 19

A transverse wave traveling along a string transports energy at a rate r. If we want to double this rate, we could

Accepted Answer

A)  increase the amplitude of the wave by a factor of 8. 
B)  increase the amplitude of the wave by a factor of 4. 
C)  increase the amplitude of the wave by a factor of 2. 
D)  increase the amplitude by a factor of   . 
E)  increase the amplitude by a factor of   . 
A)  increase the amplitude of the wave by a factor of 8. 
B)  increase the amplitude of the wave by a factor of 4. 
C)  increase the amplitude of the wave by a factor of 2. 
D)  increase the amplitude by a factor of   . 
E)  increase the amplitude by a factor of   .

Question 20

The intensity of sunlight falling on the earth is about 1.4 kW/m2 (before any gets absorbed by our atmosphere). At what rate does the sun emit light energy? (The earth-sun distance = 1.5 × 108 km and the earth's radius = 6.4 × 103 km.)

Accepted Answer

A)  4.0 × 1026 W 
B)  3.2 × 1022 W 
C)  7.2 × 1014 W 
D)  7.6 × 108 W 
A)  4.0 × 1026 W 
B)  3.2 × 1022 W 
C)  7.2 × 1014 W 
D)  7.6 × 108 W

Exam 14: Mechanical Waves

In the figure, which of the curves best represents the variation of wave speed as a function of tension for transverse waves on a stretched string?

A 6.0-m wire with a mass of 50 g, is under tension. A transverse wave, for which the frequency is 810 Hz, the wavelength is 0.40 m, and the amplitude is 4.0 mm, is propagating on the wire. The time for a crest of this wave to travel the length of the wire is closest to

A 2.0-m string is fixed at both ends and tightened until the wave speed is 78m/s. What is the frequency of the standing wave shown in the figure?

When a weight W is hanging from a light vertical string, the speed of pulses on the string is V. If a second weight W is added without stretching the string, the speed of pulses on this string will now become

A 6.00-m long rope is under a tension of 600 N. Waves travel along this rope at 40.0 m/s. What is the mass of the rope?

Standing waves of frequency 57 Hz are produced on a string that has mass per unit length 0.0160 kg/m. With what tension must the string be stretched between two supports if adjacent nodes in the standing wave are to be 0.71 meters apart?

For the wave shown in the figure, the frequency is

A standing wave is oscillating at 690 Hz on a string, as shown in the figure. What is the speed of traveling waves on this string?

A thin 2.00-m string of mass 50.0 g is fixed at both ends and under a tension of 70.0 N. If it is set into small-amplitude oscillation, what is the frequency of the first harmonic mode?

A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thinner and lighter. What is the orientation of the reflected and transmitted pulses?

Consider the waves on a vibrating guitar string and the sound waves the guitar produces in the surrounding air. The string waves and the sound waves must have the same

A transverse wave is traveling on a string stretched along the horizontal x-axis. The equation for the vertical displacement y of the string is given by y = 0.0020 cos[π(15x - 52t)], where all quantities are in SI units. The maximum speed of a particle of the string is closest to

The figure shows the displacement y of a traveling wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. How fast is the wave traveling?

The figure shows the displacement y of a wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. Determine the frequency of the wave.

A 8.0-m long wire with a mass of 10 g is under tension. A transverse wave for which the frequency is 570 Hz, the wavelength is 0.10 m, and the amplitude is 3.7 mm is propagating on the wire. The maximum transverse acceleration of a point on a wire is closest to

A transverse wave traveling along a string transports energy at a rate r. If we want to double this rate, we could

The intensity of sunlight falling on the earth is about 1.4 kW/m2 (before any gets absorbed by our atmosphere). At what rate does the sun emit light energy? (The earth-sun distance = 1.5 × 108 km and the earth's radius = 6.4 × 103 km.)

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The intensity of sunlight falling on the earth is about 1.4 kW/m2 (before any gets absorbed by our atmosphere). At what rate does the sun emit light energy? (The earth-sun distance = 1.5 × 10⁸ km and the earth's radius = 6.4 × 10³ km.)