Question 1

The figure represents a wire of length L, fixed at both ends, vibrating in several harmonics. The 3rd harmonic is shown in

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
E)  5

Question 2

A stationary wave of amplitude A and period T exists in a rope. At a particular instant, the configuration of the rope is as shown. At an instant  T later, the configuration of the rope is

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
E)  5

Question 3

Of the sound sources shown, that which is vibrating with its first harmonic is

Accepted Answer

A)  the whistle. 
B)  the organ pipe. 
C)  the vibrating string. 
D)  the vibrating rod. 
E)  None of these is correct.

Question 4

In a pipe that is open at one end and closed at the other and that has a fundamental frequency of 256 Hz, which of the following frequencies cannot be produced?

Accepted Answer

A)  768 Hz 
B)  1.28 kHz 
C)  5.12 kHz 
D)  19.7 kHz 
E)  all of these can be produced

Question 5

The wave function y(x,t) for a standing wave on a string fixed at both ends is given by y(x,t) = 0.080 sin 6.0x cos 600t where the units are SI. The amplitudes of the traveling wave that result in this standing wave are

Accepted Answer

A)  0.04 m 
B)  0.08 m 
C)  0.02 m 
D)  0.16 m 
E)  impossible to tell given this information about the standing wave.

Question 6

Of the sound sources shown, that which is vibrating with its first harmonic is the

Accepted Answer

A)  whistle. 
B)  organ pipe. 
C)  vibrating string. 
D)  vibrating rod. 
E)  vibrating spring.

Question 7

Wire A is the same mass per unit length as wire B. However wire A is twice as long as wire B and has three times as much tension on it. Calculate the fundamental frequency of wire A divided by wire B.

Accepted Answer

A)  0.87 
B)  0.66 
C)  0.43 
D)  0.75 
E)  1.50

Question 8

A string fixed at both ends is driven by a tuning fork to produce standing waves. If the tension in the string is increased,

Accepted Answer

A)  the frequency increases. 
B)  the frequency decreases and the wave velocity remains constant. 
C)  the wavelength decreases. 
D)  the wave velocity increases. 
E)  the wave velocity decreases.

Question 9

Two loudspeakers S1 and S2, 3.0 m apart, emit the same single-frequency tone in phase at the speakers. A listener directly in front of speaker S1 notices that the intensity is a minimum when she is 4.0 m from that speaker (see figure). The listener now walks around speaker S1 in an arc of a circle, staying 4.0 m from that speaker but increasing her distance from the other speaker. How far is she from speaker S2 when she notices the first maximum in the sound intensity? The speed of sound in air is 340 m/s.

Accepted Answer

A)  4.5 m 
B)  5.0 m 
C)  5.5 m 
D)  6.0 m 
E)  6.5 m

Question 10

A string fixed at both ends is 50.0 cm long and has a tension that causes the frequency of its fundamental to be 262 Hz. If the tension is increased by 4%, what does the fundamental frequency become?

Accepted Answer

A)  252 Hz 
B)  257 Hz 
C)  264 Hz 
D)  267 Hz 
E)  272 Hz

Question 11

If two identical waves with the same phase are added, the result is

Accepted Answer

A)  a wave with the same frequency but twice the amplitude. 
B)  a wave with the same amplitude but twice the frequency. 
C)  a wave with zero amplitude. 
D)  a wave with zero frequency. 
E)  This problem cannot be solved without knowing the wavelengths of the two waves.

Question 12

Two whistles produce sounds with wavelengths 3.40 m and 3.30 m. What is the beat frequency produced? (the speed of sound is 340 m/s)

Accepted Answer

A)  0.1 Hz 
B)  1.0 Hz 
C)  2.0 Hz 
D)  3.0 Hz 
E)  4.0 Hz

Question 13

Middle C on a piano has a frequency of 262 Hz. Sometimes it is said that middle C is actually 28 = 256 Hz, and tuning forks are made with this frequency. How many beats per second would be heard if such a tuning fork were sounded simultaneously with the middle C of a (well-tuned) piano?

Accepted Answer

A)  3 
B)  6 
C)  12 
D)  4 
E)  8

Question 14

A string with mass density equal to 0.0025 kg/m is fixed at both ends and at a tension of 290 N. Resonant frequencies are found at 558 Hz and the next one at 744 Hz. What is the length of the wire?

Accepted Answer

A)  0.8 m 
B)  1.6 m 
C)  3.2 m 
D)  1.2 m 
E)  0.4 m

Question 15

The standing waves on a string of length L that is fixed at both ends have a speed v. The three lowest frequencies of vibration are

Accepted Answer

A)  v/L, 2v/L, and 3v/L 
B)  v/2L, v/L, and 3v/2L 
C)  $\lambda$/2, $\lambda$, and 3$\lambda$/2 
D)  L/v, 2L/v, and 3L/v 
E)  $\lambda$/3, 2$\lambda$/3, and 3$\lambda$/3

Question 16

A vibrating tuning fork of 300 Hz is held above a tube filled with water. The first resonance is heard when the water level is lowered by 26.1 cm. A second tuning fork of 400 Hz is held above the tube, and its first resonance occurs when the water level is lowered by 19.3 cm from the top. Calculate a value for the speed of sound. (Hint: remember the small end correction $\Delta$L at the top of the tube.)

Accepted Answer

A)  333 m/s 
B)  343 m/s 
C)  325 m/s 
D)  315 m/s 
E)  338 m/s

Question 17

One  source of sound is at A and another is at B. The two sources are in phase. The distance AB = 10.0 m. The frequency of the sound waves from both sources is 1000 Hz, and both have the same amplitude. The speed of sound in air is 330 m/s. A receiver is at point C, and AB is perpendicular to AC. The greatest distance AC for which the signal at C is a minimum is

Accepted Answer

A)  33.0 cm 
B)  152 m 
C)  330 m 
D)  303 m 
E)  100 m

Question 18

A wave on a string has a frequency of 100 Hz and travels at a speed of 24 m/s. The minimum distance between two points with a phase difference of 60º is

Accepted Answer

A)  0.040 m 
B)  0.12 m 
C)  0.14 m 
D)  0.24 m 
E)  25 m

Question 19

The figure shows a wave on a string approaching its fixed end at a wall. When the wave reaches the wall and is reflected, a standing wave is set up in the string. One will observe a node at position

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
E)  5

Question 20

The ratio of the fundamental frequency (first harmonic) of an open pipe to that of a closed pipe of the same length is

Accepted Answer

A)  2:1 
B)  7:8 
C)  4:5 
D)  3:2 
E)  1:2

Exam 16: Superposition and Standing Waves

The figure represents a wire of length L, fixed at both ends, vibrating in several harmonics. The 3rd harmonic is shown in

A stationary wave of amplitude A and period T exists in a rope. At a particular instant, the configuration of the rope is as shown. At an instant T later, the configuration of the rope is

Of the sound sources shown, that which is vibrating with its first harmonic is

In a pipe that is open at one end and closed at the other and that has a fundamental frequency of 256 Hz, which of the following frequencies cannot be produced?

The wave function y(x,t) for a standing wave on a string fixed at both ends is given by y(x,t) = 0.080 sin 6.0x cos 600t where the units are SI. The amplitudes of the traveling wave that result in this standing wave are

Of the sound sources shown, that which is vibrating with its first harmonic is the

Wire A is the same mass per unit length as wire B. However wire A is twice as long as wire B and has three times as much tension on it. Calculate the fundamental frequency of wire A divided by wire B.

A string fixed at both ends is driven by a tuning fork to produce standing waves. If the tension in the string is increased,

A string fixed at both ends is 50.0 cm long and has a tension that causes the frequency of its fundamental to be 262 Hz. If the tension is increased by 4%, what does the fundamental frequency become?

If two identical waves with the same phase are added, the result is

Two whistles produce sounds with wavelengths 3.40 m and 3.30 m. What is the beat frequency produced? (the speed of sound is 340 m/s)

Middle C on a piano has a frequency of 262 Hz. Sometimes it is said that middle C is actually 2⁸ = 256 Hz, and tuning forks are made with this frequency. How many beats per second would be heard if such a tuning fork were sounded simultaneously with the middle C of a (well-tuned) piano?

A string with mass density equal to 0.0025 kg/m is fixed at both ends and at a tension of 290 N. Resonant frequencies are found at 558 Hz and the next one at 744 Hz. What is the length of the wire?

The standing waves on a string of length L that is fixed at both ends have a speed v. The three lowest frequencies of vibration are

A wave on a string has a frequency of 100 Hz and travels at a speed of 24 m/s. The minimum distance between two points with a phase difference of 60º is

The figure shows a wave on a string approaching its fixed end at a wall. When the wave reaches the wall and is reflected, a standing wave is set up in the string. One will observe a node at position

The ratio of the fundamental frequency (first harmonic) of an open pipe to that of a closed pipe of the same length is