Question 1

For a diffraction horn loudspeaker, the sound emerges through a rectangular opening.The width of a diffraction horn is 0.14 m.If the speed of sound in air is 343 m/s, at what frequency is the diffraction angle $\theta$ equal to 35°?

Accepted Answer

A) 3300 Hz 
B) 4300 Hz 
C) 6300 Hz 
D) 7700 Hz 
E) 9200 Hz

Question 2

Two traveling pulses on a rope move toward each other at a speed of 1.0 m/s.The waves have the same amplitude.The drawing shows the position of the waves at time t = 0 s.Which one of the following drawings depicts the waves on the rope at t = 2.0 s?

Accepted Answer

A) a 
B) b 
C) c 
D) d 
E) e

Question 3

A cylindrical tube sustains a fundamental frequency f1 when both of its ends are open.A second cylindrical tube with one end closed has the same fundamental frequency.What is the ratio of the length of the second tube to that of the first, L2/L1?

Accepted Answer

A) 0.5 
B) 4 
C) 2 
D) 0.25 
E) 1

Question 4

A pebble is dropped in a lake; and it produces ripples with a frequency of 0.50 Hz.When should a second pebble be dropped at the same place to produce destructive interference?

Accepted Answer

A) 0.50 s after the first 
B) 0.75 s after the first 
C) 1.0 s after the first 
D) 1.5 s after the first 
E) 2.0 s after the first

Question 5

17-2
Two loudspeakers are located 3.0 m apart on the stage of an auditorium.A listener at point P is seated 19.0 m from one speaker and 15.0 m from the other.A signal generator drives the speakers in phase with the same amplitude and frequency.The wave amplitude at P due to each speaker alone is A.The frequency is then varied between 30 Hz and 400 Hz.The speed of sound is 343 m/s.
-Determine the value of the maximum amplitude in terms of A.

Accepted Answer

A) 2.0A 
B) 2.5A 
C) 3.0A 
D) 4.0A 
E) 5.0A

Question 6

What is the wavelength of the first harmonic?

Accepted Answer

A) 0.75 m 
B) 1.50 m 
C) 3.00 m 
D) 6.00 m 
E) 12.0 m

Question 7

17-5
A string with a length of 3.0 m has two adjacent resonances at frequencies 112 Hz and 140 Hz.
-Determine the wavelength of the 140 Hz resonance.

Accepted Answer

A) 0.30 m 
B) 0.60 m 
C) 1.2 m 
D) 1.5 m 
E) 1.8 m

Question 8

Water waves approach an aperture.The resulting patterns are shown for two different cases, A and B, in which the wavelength and aperture size are varied.  Which one of the following statements concerning these cases is true?

Accepted Answer

A) Neither figure shows diffraction.In both cases, the wavelength is much smaller than the aperture. 
B) Diffraction occurs in A, but not in B because the wavelength in A is much smaller than the aperture. 
C) Diffraction occurs in B, but not in A because the wavelength in B is much smaller than the aperture. 
D) Both figures show diffraction.In both cases, the wavelengths are approximately the same size as the aperture. 
E) Diffraction occurs in B, but not in A because the wavelength in B is approximately the same size as the aperture.

Question 9

One string on a guitar is exactly in tune.The guitarist uses this string to produce a tone with a frequency of 196 Hz by pressing down at the proper fret.An adjacent string can also be used to produce this tone without being pressed against a fret.However, this adjacent string is out of tune and produces a tone that sounds lower in frequency than the other tone.When the tones are produced simultaneously, the beat frequency is 5.0 Hz.What frequency does the adjacent string produce?

Accepted Answer

A) 196 Hz 
B) 191 Hz 
C) 171 Hz 
D) 201 Hz 
E) 186 Hz

Question 10

17-5
A string with a length of 3.0 m has two adjacent resonances at frequencies 112 Hz and 140 Hz.
-Determine the fundamental frequency of the string.

Accepted Answer

A) 14 Hz 
B) 28 Hz 
C) 42 Hz 
D) 56 Hz 
E) 70 Hz

Question 11

17-2
Two loudspeakers are located 3.0 m apart on the stage of an auditorium.A listener at point P is seated 19.0 m from one speaker and 15.0 m from the other.A signal generator drives the speakers in phase with the same amplitude and frequency.The wave amplitude at P due to each speaker alone is A.The frequency is then varied between 30 Hz and 400 Hz.The speed of sound is 343 m/s.
-At what frequency or frequencies will the listener at P hear a maximum intensity?

Accepted Answer

A) 170 Hz only 
B) 113 Hz and 226 Hz 
C) 86 Hz, 170 Hz, 257, and 343 Hz 
D) 57 Hz, 114 Hz, 171 Hz, 228 Hz, 285, 342, and 399 Hz 
E) 43 Hz, 85 Hz, 128 Hz, 170 Hz, 213 Hz, 257 Hz, 298, 344, and 387 Hz

Question 12

17-3
Vibrations with frequency 6.00 × 10S1U1P12 S1S1P0Hz are established on a 1.33-m length of string that is clamped at both ends.The speed of waves on the string is 4.00 × 10S1U1P12 S1S1P0m/s.
-How many antinodes are observed for the resulting standing wave pattern?

Accepted Answer

A) 2 
B) 3 
C) 4 
D) 5 
E) 6

Question 13

A rope of length L is clamped at both ends.Which one of the following is not a possible wavelength for standing waves on this rope?

Accepted Answer

A) L/2 
B) 2L/3 
C) L 
D) 2L 
E) 4L

Question 14

A guitar string produces 4 beats/s when sounded with a 250 Hz tuning fork and 9 beats per second when sounded with a 255 Hz tuning fork.What is the vibrational frequency of the string?

Accepted Answer

A) 240 Hz 
B) 246 Hz 
C) 254 Hz 
D) 259 Hz 
E) 263 Hz

Question 15

A guitar string has a linear density of 8.30 × 10-4 kg/m and a length of 0.660 m.The tension in the string is 56.7 N.When the fundamental frequency of the string is sounded with a 196.0-Hz tuning fork, what beat frequency is heard?

Accepted Answer

A) 6 Hz 
B) 4 Hz 
C) 12 Hz 
D) 8 Hz 
E) 2 Hz

Question 16

17-4
A 6.00-m long string sustains a three-loop standing wave pattern as shown.The wave speed is 2.00 × 10S1U1P12 S1S1P0m/s. 
-What is the lowest possible frequency for standing waves on this string?

Accepted Answer

A) 50.0 Hz 
B) 33.3 Hz 
C) 25.0 Hz 
D) 16.7 Hz 
E) 8.33 Hz

Question 17

17-6
The figures show standing waves of sound in six organ pipes of the same length.Each pipe has one end open and the other end closed.Note: some of the figures show situations that are not possible. 
-Which one of the pipes emits sound with the lowest frequency?

Accepted Answer

A) 1 
B) 2 
C) 3 
D) 4 
E) 6

Question 18

17-4
A 6.00-m long string sustains a three-loop standing wave pattern as shown.The wave speed is 2.00 × 10S1U1P12 S1S1P0m/s. 
-What is the frequency of vibration?

Accepted Answer

A) 25.0 Hz 
B) 33.0 Hz 
C) 50.0 Hz 
D) 75.0 Hz 
E) 1.00 × 102 Hz

Question 19

Two pulses of identical shape travel toward each other in opposite directions on a string, as shown in the drawing.Which one of the following statements concerning this situation is true?

Accepted Answer

A) The pulses will reflect from each other. 
B) The pulses will diffract from each other. 
C) The pulses will interfere to produce a standing wave. 
D) The pulses will pass through each other and produce beats. 
E) As the pulses pass through each other, they will interfere destructively.

Question 20

17-5
A string with a length of 3.0 m has two adjacent resonances at frequencies 112 Hz and 140 Hz.
-Determine the speed of the waves on the string vibrating at 140 Hz..

Accepted Answer

A) 28 m/s 
B) 42 m/s 
C) 56 m/s 
D) 140 m/s 
E) 168 m/s

Exam 17: The Principle of Linear Superposition and Interference Phenomena

For a diffraction horn loudspeaker, the sound emerges through a rectangular opening.The width of a diffraction horn is 0.14 m.If the speed of sound in air is 343 m/s, at what frequency is the diffraction angle $\theta$ equal to 35°?

Two traveling pulses on a rope move toward each other at a speed of 1.0 m/s.The waves have the same amplitude.The drawing shows the position of the waves at time t = 0 s.Which one of the following drawings depicts the waves on the rope at t = 2.0 s?

A cylindrical tube sustains a fundamental frequency f₁ when both of its ends are open.A second cylindrical tube with one end closed has the same fundamental frequency.What is the ratio of the length of the second tube to that of the first, L₂/L₁?

A pebble is dropped in a lake; and it produces ripples with a frequency of 0.50 Hz.When should a second pebble be dropped at the same place to produce destructive interference?

What is the wavelength of the first harmonic?

17-5 A string with a length of 3.0 m has two adjacent resonances at frequencies 112 Hz and 140 Hz. -Determine the wavelength of the 140 Hz resonance.

17-5 A string with a length of 3.0 m has two adjacent resonances at frequencies 112 Hz and 140 Hz. -Determine the fundamental frequency of the string.

17-3 Vibrations with frequency 6.00 × 10²Hz are established on a 1.33-m length of string that is clamped at both ends.The speed of waves on the string is 4.00 × 10²m/s. -How many antinodes are observed for the resulting standing wave pattern?

A rope of length L is clamped at both ends.Which one of the following is not a possible wavelength for standing waves on this rope?

A guitar string produces 4 beats/s when sounded with a 250 Hz tuning fork and 9 beats per second when sounded with a 255 Hz tuning fork.What is the vibrational frequency of the string?

A guitar string has a linear density of 8.30 × 10^-⁴ kg/m and a length of 0.660 m.The tension in the string is 56.7 N.When the fundamental frequency of the string is sounded with a 196.0-Hz tuning fork, what beat frequency is heard?

17-4 A 6.00-m long string sustains a three-loop standing wave pattern as shown.The wave speed is 2.00 × 10²m/s. -What is the lowest possible frequency for standing waves on this string?

17-6 The figures show standing waves of sound in six organ pipes of the same length.Each pipe has one end open and the other end closed.Note: some of the figures show situations that are not possible. -Which one of the pipes emits sound with the lowest frequency?

17-4 A 6.00-m long string sustains a three-loop standing wave pattern as shown.The wave speed is 2.00 × 10²m/s. -What is the frequency of vibration?

17-5 A string with a length of 3.0 m has two adjacent resonances at frequencies 112 Hz and 140 Hz. -Determine the speed of the waves on the string vibrating at 140 Hz..

Exam 17: The Principle of Linear Superposition and Interference Phenomena

For a diffraction horn loudspeaker, the sound emerges through a rectangular opening.The width of a diffraction horn is 0.14 m.If the speed of sound in air is 343 m/s, at what frequency is the diffraction angle θ\thetaθ equal to 35°?

Two traveling pulses on a rope move toward each other at a speed of 1.0 m/s.The waves have the same amplitude.The drawing shows the position of the waves at time t = 0 s.Which one of the following drawings depicts the waves on the rope at t = 2.0 s?

A cylindrical tube sustains a fundamental frequency f1 when both of its ends are open.A second cylindrical tube with one end closed has the same fundamental frequency.What is the ratio of the length of the second tube to that of the first, L2/L1?

A pebble is dropped in a lake; and it produces ripples with a frequency of 0.50 Hz.When should a second pebble be dropped at the same place to produce destructive interference?

What is the wavelength of the first harmonic?

17-5 A string with a length of 3.0 m has two adjacent resonances at frequencies 112 Hz and 140 Hz. -Determine the wavelength of the 140 Hz resonance.

Water waves approach an aperture.The resulting patterns are shown for two different cases, A and B, in which the wavelength and aperture size are varied. Which one of the following statements concerning these cases is true?

17-5 A string with a length of 3.0 m has two adjacent resonances at frequencies 112 Hz and 140 Hz. -Determine the fundamental frequency of the string.

17-3 Vibrations with frequency 6.00 × 102 Hz are established on a 1.33-m length of string that is clamped at both ends.The speed of waves on the string is 4.00 × 102 m/s. -How many antinodes are observed for the resulting standing wave pattern?

A rope of length L is clamped at both ends.Which one of the following is not a possible wavelength for standing waves on this rope?

A guitar string produces 4 beats/s when sounded with a 250 Hz tuning fork and 9 beats per second when sounded with a 255 Hz tuning fork.What is the vibrational frequency of the string?

A guitar string has a linear density of 8.30 × 10-4 kg/m and a length of 0.660 m.The tension in the string is 56.7 N.When the fundamental frequency of the string is sounded with a 196.0-Hz tuning fork, what beat frequency is heard?

17-4 A 6.00-m long string sustains a three-loop standing wave pattern as shown.The wave speed is 2.00 × 102 m/s. -What is the lowest possible frequency for standing waves on this string?

17-6 The figures show standing waves of sound in six organ pipes of the same length.Each pipe has one end open and the other end closed.Note: some of the figures show situations that are not possible. -Which one of the pipes emits sound with the lowest frequency?

17-4 A 6.00-m long string sustains a three-loop standing wave pattern as shown.The wave speed is 2.00 × 102 m/s. -What is the frequency of vibration?

Two pulses of identical shape travel toward each other in opposite directions on a string, as shown in the drawing.Which one of the following statements concerning this situation is true?

17-5 A string with a length of 3.0 m has two adjacent resonances at frequencies 112 Hz and 140 Hz. -Determine the speed of the waves on the string vibrating at 140 Hz..

For a diffraction horn loudspeaker, the sound emerges through a rectangular opening.The width of a diffraction horn is 0.14 m.If the speed of sound in air is 343 m/s, at what frequency is the diffraction angle $\theta$ equal to 35°?

A cylindrical tube sustains a fundamental frequency f₁ when both of its ends are open.A second cylindrical tube with one end closed has the same fundamental frequency.What is the ratio of the length of the second tube to that of the first, L₂/L₁?

17-3 Vibrations with frequency 6.00 × 10²Hz are established on a 1.33-m length of string that is clamped at both ends.The speed of waves on the string is 4.00 × 10²m/s. -How many antinodes are observed for the resulting standing wave pattern?

A guitar string has a linear density of 8.30 × 10^-⁴ kg/m and a length of 0.660 m.The tension in the string is 56.7 N.When the fundamental frequency of the string is sounded with a 196.0-Hz tuning fork, what beat frequency is heard?

17-4 A 6.00-m long string sustains a three-loop standing wave pattern as shown.The wave speed is 2.00 × 10²m/s. -What is the lowest possible frequency for standing waves on this string?

17-4 A 6.00-m long string sustains a three-loop standing wave pattern as shown.The wave speed is 2.00 × 10²m/s. -What is the frequency of vibration?