Question 1

Sound has a velocity of 335 m/s in air. For an air column that is closed at both ends to resonate to a frequency of 528 Hz, the length of the air column could be

Accepted Answer

A)  79.2 cm 
B)  55.5 cm 
C)  47.5 cm 
D)  31.7 cm 
E)  15.8 cm

Question 2

A pipe produces successive harmonics at 300 Hz and 350 Hz. Calculate the length of the pipe and state whether it is closed at one end or not. Assume the speed of sound to be 340 m/s.

Accepted Answer

A)  1.7 m$~~~~~~~~$Closed one end 
B)  3.4 m$~~~~~~~~$Open both ends 
C)  4.0 m$~~~~~~~~$Closed one end 
D)  8.0 m$~~~~~~~~$Closed one end 
E)  4.0 m$~~~~~~~~$Open both ends

Question 3

The three curves show the harmonics of a pipe that is closed one end and open the other end. The fundamental frequency is fo. The three harmonics are

Accepted Answer

A)  fo, 2fo, 3fo 
B)  fo, 5fo, 7fo 
C)  fo, 4fo, 6fo 
D)  fo, 3fo, 4fo 
E)  fo, 6fo, 8fo

Question 4

Two identical loudspeakers are driven in phase by the same amplifier. The speakers are positioned a distance of 3.2 m apart. A person stands 4.1 m away from one speaker and 4.8 m away from the other. Calculate the second lowest frequency that results in destructive interference at the point where the person is standing. Assume the speed of sound to be 340 m/s.

Accepted Answer

A)  245 Hz 
B)  735 Hz 
C)  1225 Hz 
D)  490 Hz 
E)  1470 Hz

Question 5

The standing waves in air in a pipe of length L that is open at both ends have a speed v. The frequencies of the three lowest harmonics 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 6

The sources S1 and S2 are coherent sources, and the circular arcs represent wave crests. The position that corresponds to a path difference of two wavelengths is

Accepted Answer

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

Question 7

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. To what harmonic does the 558 Hz resonance correspond?

Accepted Answer

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

Question 8

A microphone is placed at the node of a standing sound wave. What does the microphone pick up?

Accepted Answer

A)  A constant and very high intensity sound. 
B)  A constant and very low intensity sound. 
C)  A varying high intensity sound. 
D)  A varying low intensity sound. 
E)  Unable to tell.

Question 9

The air column in an organ pipe, which is closed at one end, is vibrating in such a way as to produce the second harmonic. A pressure node and displacement node, respectively, occur at

Accepted Answer

A)  1 and 3 
B)  1 and 5 
C)  7 and 4 
D)  7 and 5 
E)  5 and 3

Question 10

The air in a closed organ pipe vibrates as shown. The length of the pipe is 3.0 m. The frequency of vibration is 80 Hz. The speed of sound in the pipe is approximately

Accepted Answer

A)  80 m/s 
B)  0.16 km/s 
C)  0.24 km/s 
D)  0.32 km/s 
E)  0.96 km/s

Question 11

A vibrating tuning fork of frequency 640 Hz is held above a tube filled with water. Assume the speed of sound to be 330 m/s. As the water level is lowered, consecutive maxima in intensity are observed at intervals of about

Accepted Answer

A)  12.9 cm 
B)  19.4 cm 
C)  25.8 cm 
D)  51.7 cm 
E)  194 cm

Question 12

What is the third harmonic of an open-both-ends organ pipe of length 1.5 m? Assume the speed of sound to be 340 m/s.

Accepted Answer

A)  229 Hz 
B)  340 Hz 
C)  457 Hz 
D)  686 Hz 
E)  none of the above

Question 13

Two waves with the same frequency and wavelength but with different amplitudes are added. If A1 = 2A2 and the waves are 180º out of phase, then the amplitude of the resultant wave is

Accepted Answer

A)  zero. 
B)  the same as A1. 
C)  the same as A2. 
D)  equal to A1 + A2. 
E)  coherent.

Question 14

The frequency spectrum of the composite wave 1 + 3 + 5 shown is best represented by

Accepted Answer

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

Question 15

The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is closest to

Accepted Answer

A)  2.0 mm 
B)  1.8 mm 
C)  1.4 mm 
D)  1.0 mm 
E)  zero

Question 16

The fundamental frequency of a vibrating string is f1. If the tension in the string is doubled, the fundamental frequency becomes

Accepted Answer

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

Question 17

The figure represents a string of length L, fixed at both ends, vibrating in several harmonics. The 4th harmonic is shown in

Accepted Answer

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

Question 18

A vibrating tuning fork of frequency 1080 Hz is held above a tube filled with water. Assume the speed of sound to be 330 m/s. As the water level is lowered, consecutive maxima in intensity are observed at intervals of about

Accepted Answer

A)  7.65 cm 
B)  15.3 cm 
C)  23.0 cm 
D)  30.6 cm 
E)  53.6 cm

Question 19

The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is

Accepted Answer

A)  2.0 mm 
B)  1.8 mm 
C)  1.4 mm 
D)  1.0 mm 
E)  0.83 mm

Question 20

A string fixed at both ends is vibrating in a standing wave. There are three nodes between the ends of the string, not including those on the ends. The string is vibrating at a frequency that is its

Accepted Answer

A)  fundamental. 
B)  second harmonic. 
C)  third harmonic. 
D)  fourth harmonic. 
E)  fifth harmonic.

Exam 16: Superposition and Standing Waves

Sound has a velocity of 335 m/s in air. For an air column that is closed at both ends to resonate to a frequency of 528 Hz, the length of the air column could be

A pipe produces successive harmonics at 300 Hz and 350 Hz. Calculate the length of the pipe and state whether it is closed at one end or not. Assume the speed of sound to be 340 m/s.

The three curves show the harmonics of a pipe that is closed one end and open the other end. The fundamental frequency is f_o. The three harmonics are

The standing waves in air in a pipe of length L that is open at both ends have a speed v. The frequencies of the three lowest harmonics are

The sources S₁ and S₂ are coherent sources, and the circular arcs represent wave crests. The position that corresponds to a path difference of two wavelengths is

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. To what harmonic does the 558 Hz resonance correspond?

A microphone is placed at the node of a standing sound wave. What does the microphone pick up?

The air column in an organ pipe, which is closed at one end, is vibrating in such a way as to produce the second harmonic. A pressure node and displacement node, respectively, occur at

The air in a closed organ pipe vibrates as shown. The length of the pipe is 3.0 m. The frequency of vibration is 80 Hz. The speed of sound in the pipe is approximately

A vibrating tuning fork of frequency 640 Hz is held above a tube filled with water. Assume the speed of sound to be 330 m/s. As the water level is lowered, consecutive maxima in intensity are observed at intervals of about

What is the third harmonic of an open-both-ends organ pipe of length 1.5 m? Assume the speed of sound to be 340 m/s.

Two waves with the same frequency and wavelength but with different amplitudes are added. If A₁ = 2A₂ and the waves are 180º out of phase, then the amplitude of the resultant wave is

The frequency spectrum of the composite wave 1 + 3 + 5 shown is best represented by

The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is closest to

The fundamental frequency of a vibrating string is f₁. If the tension in the string is doubled, the fundamental frequency becomes

The figure represents a string of length L, fixed at both ends, vibrating in several harmonics. The 4th harmonic is shown in

A vibrating tuning fork of frequency 1080 Hz is held above a tube filled with water. Assume the speed of sound to be 330 m/s. As the water level is lowered, consecutive maxima in intensity are observed at intervals of about

The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is

A string fixed at both ends is vibrating in a standing wave. There are three nodes between the ends of the string, not including those on the ends. The string is vibrating at a frequency that is its