Question 1

In a resonating pipe that is open at one end and closed at the other, there

Accepted Answer

A) are displacement nodes at each end. 
B) are displacement antinodes at each end. 
C) is a displacement node at the open end and a displacement antinode at the closed end. 
D) is a displacement node at the closed end and a displacement antinode at the open end. 
A) are displacement nodes at each end. 
B) are displacement antinodes at each end. 
C) is a displacement node at the open end and a displacement antinode at the closed end. 
D) is a displacement node at the closed end and a displacement antinode at the open end.

Question 2

A 2.0-g string that is 0.67 m long is under tension. The string vibrates at 700 Hz tone in its third harmonic, and this vibration causes a sound wave. What is the wavelength of the sound? The speed of sound in air is 344 m/s.

Accepted Answer

A) 0.49 
B) 0.55 
C) 0.61 
D) 0.67 
E) 0.45 
A) 0.49 
B) 0.55 
C) 0.61 
D) 0.67 
E) 0.45

Question 3

The lowest tone to resonate in a pipe of length L that is closed at one end but open at the other end is 200 Hz. Which one of the following frequencies will not resonate in that pipe?

Accepted Answer

A) 200 Hz 
B) 400 Hz 
C) 600 Hz 
D) 1000 Hz 
E) 1400 Hz 
A) 200 Hz 
B) 400 Hz 
C) 600 Hz 
D) 1000 Hz 
E) 1400 Hz

Question 4

What is the frequency of the fundamental mode of vibration of a steel piano wire stretched to a tension of 440 N? The wire is 0.600 m long and has a mass of 5.60 g.

Accepted Answer

A) 517 Hz 
B) 234 Hz 
C) 181 Hz 
D) 312 Hz 
E) 366 Hz 
A) 517 Hz 
B) 234 Hz 
C) 181 Hz 
D) 312 Hz 
E) 366 Hz

Question 5

A violin with string length 32 cm and string density $1.5 \mathrm {~g} / \mathrm { cm }$ resonates in its fundamental with the first overtone of a 2.0-m organ pipe with one end closed and one end open. What is the tension in the string if the speed of sound in air is 344 m/s?

Accepted Answer

A) 1000 N 
B) 110 N 
C) 450 N 
D) 4100 N 
E) 56 N 
A) 1000 N 
B) 110 N 
C) 450 N 
D) 4100 N 
E) 56 N

Question 6

Two in-phase loudspeakers are placed along a wall and are separated by a distance of 4.00 m. They emit sound with a frequency of 514 Hz. A person is standing away from the wall, in front of one of the loudspeakers. What is the closest nonzero distance from the wall the person can stand and hear constructive interference? The speed of sound in air is 343 m/s.

Accepted Answer

A) 0.34 m 
B) 0.73 m 
C) 1.2 m 
D) 1.6 m 
A) 0.34 m 
B) 0.73 m 
C) 1.2 m 
D) 1.6 m

Question 7

Two taut strings of identical mass and length are stretched with their ends fixed, but the tension in one string is 1.10 times greater than in the other. Waves on the string with the lower tension propagate at 35.2 m/s. The fundamental frequency of that string is 258 Hz. What is the beat frequency when each string is vibrating at its fundamental frequency?

Accepted Answer

A) 11.0 Hz 
B) 9.00 Hz 
C) 13.7 Hz 
D) 12.6 Hz 
E) 17.1 Hz 
A) 11.0 Hz 
B) 9.00 Hz 
C) 13.7 Hz 
D) 12.6 Hz 
E) 17.1 Hz

Question 8

One of the harmonics of a string fixed at both ends has a frequency of 52.2 Hz and the next higher harmonic has a frequency of 60.9 Hz. What is the fundamental frequency of the string?

Accepted Answer

A) 26.1 Hz 
B) 8.7 Hz 
C) 4.35 Hz 
D) 30.4 Hz 
E) 17.4 Hz 
A) 26.1 Hz 
B) 8.7 Hz 
C) 4.35 Hz 
D) 30.4 Hz 
E) 17.4 Hz

Question 9

A 4.0-g string is 0.39 m long and is under tension. The string vibrates at 600 Hz in its third harmonic. What is the tension in this string?

Accepted Answer

A) 250 N 
B) 200 N 
C) 160 N 
D) 290 N 
E) 340 N 
A) 250 N 
B) 200 N 
C) 160 N 
D) 290 N 
E) 340 N

Question 10

Consider the standing wave on a guitar string and the sound wave generated by the string as a result of this vibration. What do these two waves have in common? (There may be more than one correct choice.)

Accepted Answer

A) They have the same wavelength. 
B) They have the same speed. 
C) They have the same frequency. 
D) They have the same amplitude. 
E) They have the same period. 
A) They have the same wavelength. 
B) They have the same speed. 
C) They have the same frequency. 
D) They have the same amplitude. 
E) They have the same period.

Question 11

Two in-phase loudspeakers are 3.0 m apart. They emit sound with a frequency of 490 Hz. A microphone is placed half-way between the speakers and then moved along the line joining the two speakers until the first point of constructive interference is found. At what distance from that midpoint is that first point? The speed of sound in air is 343 m/s.

Accepted Answer

A) 0.18 m 
B) 0.35 m 
C) 0.50 m 
D) 0.70 m 
E) There is no point in that line where constructive interference occurs. 
A) 0.18 m 
B) 0.35 m 
C) 0.50 m 
D) 0.70 m 
E) There is no point in that line where constructive interference occurs.

Question 12

A 4.0-g string is 0.36 m long and is under tension. The string vibrates at 500 Hz in its third harmonic. What is the wavelength of the standing wave in the string?

Accepted Answer

A) 0.24 m 
B) 0.36 m 
C) 0.54 m 
D) 0.72 m 
E) 0.90 m 
A) 0.24 m 
B) 0.36 m 
C) 0.54 m 
D) 0.72 m 
E) 0.90 m

Question 13

The wavelengths of the sounds produced by two horns are 6.0 m and 7.0 m, respectively. What beat frequency is heard when the horns are sounded on a day when the speed of sound is 340 m/s?

Accepted Answer

A) 5 Hz 
B) 6 Hz 
C) 7 Hz 
D) 8 Hz 
A) 5 Hz 
B) 6 Hz 
C) 7 Hz 
D) 8 Hz

Question 14

Two tuning forks have frequencies of 440 and 522 Hz. What is the beat frequency if both are sounding simultaneously?

Accepted Answer

A) 962 Hz 
B) 481 Hz 
C) 82 Hz 
D) 55 Hz 
E) 41 Hz 
A) 962 Hz 
B) 481 Hz 
C) 82 Hz 
D) 55 Hz 
E) 41 Hz

Question 15

A policeman in a stationary car measures the speed of approaching cars by means of an ultrasonic device that emits a sound with a frequency of 39.6 kHz. A car is approaching him at a speed of 35.0 m/s. The wave is reflected by the car and interferes with the emitted sound producing beats. What is the frequency of the beats when the speed of sound in air is 343 m/s?

Accepted Answer

A) 5000 Hz 
B) 4500 Hz 
C) 8490 Hz 
D) 9000 Hz 
E) 4250 Hz 
A) 5000 Hz 
B) 4500 Hz 
C) 8490 Hz 
D) 9000 Hz 
E) 4250 Hz

Question 16

Two loudspeakers placed 6.00 m apart are driven in phase by an audio oscillator having a frequency range from 1908 Hz to 2471 Hz. A point P is located 4.70 m from one loudspeaker and 3.60 m from the other speaker. At what frequency of the oscillator does the sound reaching point P interfere constructively? The speed of sound is 344 m/s.

Accepted Answer

A) 2190 Hz 
B) 2420 Hz 
C) 2110 Hz 
D) 2340 Hz 
E) 2270 Hz 
A) 2190 Hz 
B) 2420 Hz 
C) 2110 Hz 
D) 2340 Hz 
E) 2270 Hz

Question 17

A standing wave of the third overtone is induced in a 1.2-m pipe that is open at one end and closed at the other end. The speed of sound in the pipe is 340 m/s.
(a)How many antinodes are there in the standing wave pattern?
(b)What is the frequency of the sound produced by the pipe in this situation?

Accepted Answer

The answer of A standing wave of the third overtone...

Question 18

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

Accepted Answer

A) 600 Hz 
B) 360 Hz 
C) 240 Hz 
D) 120 Hz 
A) 600 Hz 
B) 360 Hz 
C) 240 Hz 
D) 120 Hz

Question 19

A string of length 2.5 m is fixed at both ends. When the string vibrates at a frequency of 85 Hz, a standing wave with five loops is formed.
(a)Determine the distance between two adjacent nodes.
(b)Determine the wavelength of the waves that travel on the string.
(c)Determine the speed of traveling waves on this string.
(d)Determine the fundamental frequency of this string.

Accepted Answer

(a)0.50 m

Question 20

Two in-phase loudspeakers that emit sound with the same frequency are placed along a wall and are separated by a distance of 8.00 m. A person is standing 12.0 m away from the wall, equidistant from the loudspeakers. When the person moves 3.00 m parallel to the wall, she experiences destructive interference for the second time. What is the frequency of the sound? The speed of sound in air is 343 m/s.

Accepted Answer

A) 278 Hz 
B) 422 Hz 
C) 452 Hz 
D) 562 Hz 
E) 694 Hz 
A) 278 Hz 
B) 422 Hz 
C) 452 Hz 
D) 562 Hz 
E) 694 Hz

Exam 16: Superposition and Standing Waves

In a resonating pipe that is open at one end and closed at the other, there

A 2.0-g string that is 0.67 m long is under tension. The string vibrates at 700 Hz tone in its third harmonic, and this vibration causes a sound wave. What is the wavelength of the sound? The speed of sound in air is 344 m/s.

The lowest tone to resonate in a pipe of length L that is closed at one end but open at the other end is 200 Hz. Which one of the following frequencies will not resonate in that pipe?

What is the frequency of the fundamental mode of vibration of a steel piano wire stretched to a tension of 440 N? The wire is 0.600 m long and has a mass of 5.60 g.

A violin with string length 32 cm and string density 1.5 g/cm1.5 \mathrm {~g} / \mathrm { cm }1.5 g/cm resonates in its fundamental with the first overtone of a 2.0-m organ pipe with one end closed and one end open. What is the tension in the string if the speed of sound in air is 344 m/s?

One of the harmonics of a string fixed at both ends has a frequency of 52.2 Hz and the next higher harmonic has a frequency of 60.9 Hz. What is the fundamental frequency of the string?

A 4.0-g string is 0.39 m long and is under tension. The string vibrates at 600 Hz in its third harmonic. What is the tension in this string?

Consider the standing wave on a guitar string and the sound wave generated by the string as a result of this vibration. What do these two waves have in common? (There may be more than one correct choice.)

A 4.0-g string is 0.36 m long and is under tension. The string vibrates at 500 Hz in its third harmonic. What is the wavelength of the standing wave in the string?

The wavelengths of the sounds produced by two horns are 6.0 m and 7.0 m, respectively. What beat frequency is heard when the horns are sounded on a day when the speed of sound is 340 m/s?

Two tuning forks have frequencies of 440 and 522 Hz. What is the beat frequency if both are sounding simultaneously?

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

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A violin with string length 32 cm and string density $1.5 \mathrm {~g} / \mathrm { cm }$ resonates in its fundamental with the first overtone of a 2.0-m organ pipe with one end closed and one end open. What is the tension in the string if the speed of sound in air is 344 m/s?