Question 1

A clarinet behaves like a tube closed at one end. If its length is 1.0 m, and the velocity of sound is 344 m/s, what is its fundamental frequency (in Hz)?

Accepted Answer

A) 264 
B) 140 
C) 86 
D) 440 
E) 172 
A) 264 
B) 140 
C) 86 
D) 440 
E) 172 C

Question 2

Transverse waves y1 = A1 sin(k1x - $ \omega $1t) and y2 = A2 sin(k2x - $ \omega $2t), with A2 > A1, start at opposite ends of a long rope when t = 0. The magnitude of the maximum displacement, y, of the rope at any point is:

Accepted Answer

A) A1 -A2. 
B) A2- A1. 
C) A1 + A2. 
D)  $\left(A_{1}-A_{2}\right) \frac{k_{1}}{k_{2}}$ . 
E)  $\left(A_{2}-A_{1}\right) \frac{k_{2}}{k_{1}}$ . 
A) A1 -A2. 
B) A2- A1. 
C) A1 + A2. 
D)  $\left(A_{1}-A_{2}\right) \frac{k_{1}}{k_{2}}$ . 
E)  $\left(A_{2}-A_{1}\right) \frac{k_{2}}{k_{1}}$ . C

Question 3

Two organ pipes, a pipe of fundamental frequency 440 Hz, closed at one end, and a pipe of fundamental frequency 660 Hz, open at both ends, produce overtones. Which choice below correctly describes overtones present in both pipes?

Accepted Answer

A) After the first overtone of each pipe, every second overtone of the first pipe matches every second overtone of the second pipe. 
B) After the first overtone of each pipe, every second overtone of the first pipe matches every third overtone of the second pipe. 
C) After the first overtone of each pipe, every third overtone of the first pipe matches every second overtone of the second pipe. 
D) After the first overtone of each pipe, every second overtone of the first pipe matches every fourth overtone of the second pipe. 
E) After the first overtone of each pipe, every third overtone of the first pipe matches every fourth overtone of the second pipe. 
A) After the first overtone of each pipe, every second overtone of the first pipe matches every second overtone of the second pipe. 
B) After the first overtone of each pipe, every second overtone of the first pipe matches every third overtone of the second pipe. 
C) After the first overtone of each pipe, every third overtone of the first pipe matches every second overtone of the second pipe. 
D) After the first overtone of each pipe, every second overtone of the first pipe matches every fourth overtone of the second pipe. 
E) After the first overtone of each pipe, every third overtone of the first pipe matches every fourth overtone of the second pipe. E

Question 4

A fire engine approaches a wall at 5 m/s while the siren emits a tone of 500 Hz frequency. At the time, the speed of sound in air is 340 m/s. How many beats per second do the people on the fire engine hear?

Accepted Answer

A) 0 
B) 15 
C) 29 
D) 63 
E) 250 
A) 0 
B) 15 
C) 29 
D) 63 
E) 250

Question 5

Two harmonic waves are described by: $y_{1}=(3 \mathrm{~cm}) \sin \left(\frac{8.0}{\mathrm{~m}} x+\frac{2.0}{\mathrm{~s}} t\right)$ $y_{2}=(3 \mathrm{~cm}) \sin \left(\frac{8.0}{\mathrm{~m}} x-\frac{2.0}{\mathrm{~s}} t\right)$ What is the magnitude of the speed (in m/s) of the two travelling waves?

Accepted Answer

A) 16 
B) 4.0 
C) 8.0 
D) 0.25 
E) 2.0 
A) 16 
B) 4.0 
C) 8.0 
D) 0.25 
E) 2.0

Question 6

An organ pipe open at both ends has a radius of 4.0 cm and a length of 6.0 m. What is the frequency (in Hz) of the third harmonic? (Assume the velocity of sound is 344 m/s.)

Accepted Answer

A) 76 
B) 86 
C) 54 
D) 28 
E) 129 
A) 76 
B) 86 
C) 54 
D) 28 
E) 129

Question 7

Two point sources emit sound waves of 1.0-m wavelength. The sources, 2.0 m apart, as shown below, emit waves which are in phase with each other at the instant of emission. Where, along the line between the sources, are the waves out of phase with each other by  $\pi$ radians?

Accepted Answer

A) x = 0, 1.0 m, 2.0 m 
B) x = 0.50 m, 1.5 m 
C) x = 0.50 m, 1.0 m, 1.5 m 
D) x = 0.75 m, 1.25 m 
E) x = 0.25 m, 0.75 m, 1.25 m, 1.75 m 
A) x = 0, 1.0 m, 2.0 m 
B) x = 0.50 m, 1.5 m 
C) x = 0.50 m, 1.0 m, 1.5 m 
D) x = 0.75 m, 1.25 m 
E) x = 0.25 m, 0.75 m, 1.25 m, 1.75 m

Question 8

Which of the following frequencies could NOT be present as a standing wave in a 2-m long organ pipe open at both ends? The fundamental frequency is 85 Hz.

Accepted Answer

A) 85 Hz. 
B) 170 Hz. 
C) 255 Hz. 
D) 340 Hz. 
E) 382 Hz. 
A) 85 Hz. 
B) 170 Hz. 
C) 255 Hz. 
D) 340 Hz. 
E) 382 Hz.

Question 9

Refer to Exhibit 18-1 below.Exhibit 18-1 The figure below shows wave crests after a stone is thrown into a pond.   The phase difference in radians between points A and D is:

Accepted Answer

A) ( $\pi$.) 
B) 2 $\pi$. 
C) 3 $\pi$. 
D) 4 $\pi$. 
E) 5 $\pi$. 
A) ( $\pi$.) 
B) 2 $\pi$. 
C) 3 $\pi$. 
D) 4 $\pi$. 
E) 5 $\pi$.

Question 10

Two harmonic waves travelling in opposite directions interfere to produce a standing wave described by y = 3 sin (2x) cos 5t where x is in m and t is in s. What is the wavelength of the interfering waves?

Accepted Answer

A) 3.14 m 
B) 1.00 m 
C) 6.28 m 
D) 12.0 m 
E) 2.00 m 
A) 3.14 m 
B) 1.00 m 
C) 6.28 m 
D) 12.0 m 
E) 2.00 m

Question 11

A student wants to establish a standing wave on a wire 1.8 m long clamped at both ends. The wave speed is 540 m/s. What is the minimum frequency she should apply to set up standing waves?

Accepted Answer

The answer of A student wants to establish a standing...

Question 12

Drummers like to have high-pitched cymbals that vibrate at high frequencies. To obtain the highest frequencies, a cymbal of a fixed size should be made of a material:

Accepted Answer

A) with a low Young's modulus and a low density. 
B) with a low Young's modulus and a high density. 
C) with a high Young's modulus and a low density. 
D) with a high Young's modulus and a high density. 
E) composed of a metal-plastic laminate. 
A) with a low Young's modulus and a low density. 
B) with a low Young's modulus and a high density. 
C) with a high Young's modulus and a low density. 
D) with a high Young's modulus and a high density. 
E) composed of a metal-plastic laminate.

Question 13

A harmonic longitudinal wave propagating down a tube filled with a compressible gas has the form s(x, t) = sm cos (kx -  $ \omega $t). Its velocity can be obtained from:

Accepted Answer

A) ( $ \omega $/k) 
B) k/ $ \omega $ 
C) k 
D) ( $ \omega $) 
E) ( $ \omega $k) 
A) ( $ \omega $/k) 
B) k/ $ \omega $ 
C) k 
D) ( $ \omega $) 
E) ( $ \omega $k)

Question 14

An organ pipe open at both ends is 1.5 m long. A second organ pipe that is closed at one end and open at the other is 0.75 m long. The speed of sound in the room is 330 m/s. Which of the following sets of frequencies consists of frequencies which can be produced by both pipes?

Accepted Answer

A) 110 Hz, 220 Hz, 330 Hz 
B) 220 Hz, 440 Hz, 660 Hz 
C) 110 Hz, 330 Hz, 550 Hz 
D) 330 Hz, 440 Hz, 550 Hz 
E) 220 Hz, 660 Hz, 1 100 Hz 
A) 110 Hz, 220 Hz, 330 Hz 
B) 220 Hz, 440 Hz, 660 Hz 
C) 110 Hz, 330 Hz, 550 Hz 
D) 330 Hz, 440 Hz, 550 Hz 
E) 220 Hz, 660 Hz, 1 100 Hz

Question 15

Two waves are described by: y1 = 6 cos 180t and y2 = 6 cos 186t, (both in metres).What effective frequency does the resultant vibration have at a point?

Accepted Answer

A) 92 Hz 
B) 183 Hz 
C) 6 Hz 
D) 3 Hz 
E) 366 Hz 
A) 92 Hz 
B) 183 Hz 
C) 6 Hz 
D) 3 Hz 
E) 366 Hz

Question 16

When two organ pipes open at both ends sound a perfect fifth, such as two notes with fundamental frequencies at 440 Hz and 660 Hz, both pipes produce overtones. Which choice below correctly describes overtones present in both pipes?

Accepted Answer

A) 440, 880 and 1320 Hz. 
B) 660, 1320 and 1980 Hz. 
C) 880, 1320 and 1760 Hz. 
D) 1320, 2640 and 3960 Hz. 
E) They have no overtones in common. 
A) 440, 880 and 1320 Hz. 
B) 660, 1320 and 1980 Hz. 
C) 880, 1320 and 1760 Hz. 
D) 1320, 2640 and 3960 Hz. 
E) They have no overtones in common.

Question 17

Two harmonic waves are described by: $y_{1}=(7 m) \sin \left(\frac{5}{m} x-\frac{100}{s} t\right)$ $y_{2}=(7 \mathrm{~m}) \sin \left(\frac{5}{\mathrm{~m}} x-\frac{100}{\mathrm{~s}} t+2\right)$ What is the phase (in rad) of the resultant wave when x = t = 0?

Accepted Answer

A) 3 
B) 0 
C) 2 
D) 1 
E) 4 
A) 3 
B) 0 
C) 2 
D) 1 
E) 4

Question 18

Two harmonic waves travelling in opposite directions interfere to produce a standing wave described by y = 2 sin (4x) cos (3t) where x is in m and t is in s. What is the speed (in m/s) of the interfering waves?

Accepted Answer

A) 0.75 
B) 0.25 
C) 1.3 
D) 12 
E) 3.0 
A) 0.75 
B) 0.25 
C) 1.3 
D) 12 
E) 3.0

Question 19

Two harmonic waves travelling in opposite directions interfere to produce a standing wave described by y = 2 sin ( $\pi$x) cos (3 $\pi$t) where x is in m and t is in s. What is the distance (in m) between the first two antinodes?

Accepted Answer

A) 8 
B) 2 
C) 4 
D) 1 
E) 0.5 
A) 8 
B) 2 
C) 4 
D) 1 
E) 0.5

Question 20

Two identical strings have the same length and same mass per unit length. String B is stretched with four times as great a tension as that applied to string A. Which statement is correct for all n harmonics on the two strings, n = 1, 2, 3...?

Accepted Answer

A)    . 
B)    . 
C)    . 
D) fn,B = 2fn,A. 
E) fn,B = 4fn,A. 
A)    . 
B)    . 
C)    . 
D) fn,B = 2fn,A. 
E) fn,B = 4fn,A.

Exam 18: Superposition and Interference

A clarinet behaves like a tube closed at one end. If its length is 1.0 m, and the velocity of sound is 344 m/s, what is its fundamental frequency (in Hz)?

Transverse waves y1 = A1 sin(k1x - ω \omega ω 1t) and y2 = A2 sin(k2x - ω \omega ω 2t), with A2 > A1, start at opposite ends of a long rope when t = 0. The magnitude of the maximum displacement, y, of the rope at any point is:

Two organ pipes, a pipe of fundamental frequency 440 Hz, closed at one end, and a pipe of fundamental frequency 660 Hz, open at both ends, produce overtones. Which choice below correctly describes overtones present in both pipes?

A fire engine approaches a wall at 5 m/s while the siren emits a tone of 500 Hz frequency. At the time, the speed of sound in air is 340 m/s. How many beats per second do the people on the fire engine hear?

An organ pipe open at both ends has a radius of 4.0 cm and a length of 6.0 m. What is the frequency (in Hz) of the third harmonic? (Assume the velocity of sound is 344 m/s.)

Two point sources emit sound waves of 1.0-m wavelength. The sources, 2.0 m apart, as shown below, emit waves which are in phase with each other at the instant of emission. Where, along the line between the sources, are the waves out of phase with each other by π\piπ radians?

Which of the following frequencies could NOT be present as a standing wave in a 2-m long organ pipe open at both ends? The fundamental frequency is 85 Hz.

Refer to Exhibit 18-1 below.Exhibit 18-1 The figure below shows wave crests after a stone is thrown into a pond. The phase difference in radians between points A and D is:

Two harmonic waves travelling in opposite directions interfere to produce a standing wave described by y = 3 sin (2x) cos 5t where x is in m and t is in s. What is the wavelength of the interfering waves?

A student wants to establish a standing wave on a wire 1.8 m long clamped at both ends. The wave speed is 540 m/s. What is the minimum frequency she should apply to set up standing waves?

Drummers like to have high-pitched cymbals that vibrate at high frequencies. To obtain the highest frequencies, a cymbal of a fixed size should be made of a material:

A harmonic longitudinal wave propagating down a tube filled with a compressible gas has the form s(x, t) = sm cos (kx - ω \omega ω t). Its velocity can be obtained from:

An organ pipe open at both ends is 1.5 m long. A second organ pipe that is closed at one end and open at the other is 0.75 m long. The speed of sound in the room is 330 m/s. Which of the following sets of frequencies consists of frequencies which can be produced by both pipes?

Two waves are described by: y1 = 6 cos 180t and y2 = 6 cos 186t, (both in metres).What effective frequency does the resultant vibration have at a point?

When two organ pipes open at both ends sound a perfect fifth, such as two notes with fundamental frequencies at 440 Hz and 660 Hz, both pipes produce overtones. Which choice below correctly describes overtones present in both pipes?

Two harmonic waves travelling in opposite directions interfere to produce a standing wave described by y = 2 sin (4x) cos (3t) where x is in m and t is in s. What is the speed (in m/s) of the interfering waves?

Two harmonic waves travelling in opposite directions interfere to produce a standing wave described by y = 2 sin ( π\piπ x) cos (3 π\piπ t) where x is in m and t is in s. What is the distance (in m) between the first two antinodes?

Two identical strings have the same length and same mass per unit length. String B is stretched with four times as great a tension as that applied to string A. Which statement is correct for all n harmonics on the two strings, n = 1, 2, 3...?

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Transverse waves y1 = A1 sin(k1x - $\omega$ 1t) and y2 = A2 sin(k2x - $\omega$ 2t), with A2 > A1, start at opposite ends of a long rope when t = 0. The magnitude of the maximum displacement, y, of the rope at any point is:

A harmonic longitudinal wave propagating down a tube filled with a compressible gas has the form s(x, t) = sm cos (kx - $\omega$ t). Its velocity can be obtained from:

Two harmonic waves travelling in opposite directions interfere to produce a standing wave described by y = 2 sin ( $\pi$ x) cos (3 $\pi$ t) where x is in m and t is in s. What is the distance (in m) between the first two antinodes?