Deck 12: Sound

Question 1

The bulk modulus of water is $0.210 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$ and the density is $1000 \mathrm{~kg} / \mathrm{m}^{3}$ . The speed of sound in water is

A) $2,150 \mathrm{~m} / \mathrm{s}$
B) $2,750 \mathrm{~m} / \mathrm{s}$ .
C) $2,490 \mathrm{~m} / \mathrm{s}$ .
D) $3,100 \mathrm{~m} / \mathrm{s}$ .
E) $1,450 \mathrm{~m} / \mathrm{s}$ .

Answer 1

$1,450 \mathrm{~m} / \mathrm{s}$ .

Question 2

The speed of sound in helium is $965 \mathrm{~m} / \mathrm{s}$ . If the density of helium is $0.179 \mathrm{~kg} / \mathrm{m}^{3}$ , then what is the bulk modulus of helium?

A) $1.67 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$
B) $1.56 \times 10^{5}\mathrm{~N} / \mathrm{m}^{2}$
C) $2.40 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$
D) $2.70 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$
E) $2.20 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$

Answer 2

$1.67 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$

Question 3

The speed of sound in air at $0^{\circ} \mathrm{C}$ is $331 \mathrm{~m} / \mathrm{s}$ . If the density of air is $1.29 \mathrm{~kg} / \mathrm{m}^{3}$ , then what is the bulk modulus of air?

A) $2.50 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$
B) $2.03 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$
C) $1.68 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$
D) $1.41 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$
E) $1.15 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$

Answer 3

$1.41 \times 10^{5} \mathrm{~N} / \mathrm{m}^{2}$

Question 4

The speed of sound in air at $0^{\circ} \mathrm{C}$ is $331 \mathrm{~m} / \mathrm{s}$ . What is the speed of sound in air at a temperature of $30^{\circ} \mathrm{C}$ ?

A) $336 \mathrm{~m} / \mathrm{s}$
B) $349 \mathrm{~m} / \mathrm{s}$
C) $342 \mathrm{~m} / \mathrm{s}$
D) $340 \mathrm{~m} / \mathrm{s}$
E) $338 \mathrm{~m} / \mathrm{s}$

Question 5

The speed of sound in air at $0^{\circ} \mathrm{C}$ is $331 \mathrm{~m} / \mathrm{s}$ . What is the speed of sound in air at a temperature of $-30^{\circ} \mathrm{C}$ ?

A) $308 \mathrm{~m} / \mathrm{s}$
B) $316 \mathrm{~m} / \mathrm{s}$
C) $312 \mathrm{~m} / \mathrm{s}$
D) $310 \mathrm{~m} / \mathrm{s}$
E) $314 \mathrm{~m} / \mathrm{s}$

Question 6

The bulk modulus of mercury is $2.85 \times 1010 \mathrm{~N} / \mathrm{m}^{2}$ . If the density of mercury is $1.36 \times 104 \mathrm{~kg} / \mathrm{m}^{3}$ , then what is the speed of sound in mercury?

A) $6.91 \times 10^{-4} \mathrm{~m} / \mathrm{s}$
B) $1.45 \times 10^{3} \mathrm{~m} / \mathrm{s}$
C) $4.77 \times 10^{-7} \mathrm{~m} / \mathrm{s}$
D) $2.10 \times 10^{6} \mathrm{~m} / \mathrm{s}$
E) $2.44 \times 10^{8} \mathrm{~m} / \mathrm{s}$

Question 7

The Young's modulus of aluminum is $6.90 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$ . If the density of aluminum is $2,700 \mathrm{~kg} / \mathrm{m}^{3}$ , then what is the speed of longitudinal waves along a thin aluminum rod?

A) $5,060 \mathrm{~m} / \mathrm{s}$
B) $6,020 \mathrm{~m} / \mathrm{s}$
C) $4,850 \mathrm{~m} / \mathrm{s}$
D) $6,360 \mathrm{~m} / \mathrm{s}$
E) $5,750 \mathrm{~m} / \mathrm{s}$

Question 8

The speed of longitudinal waves in a long brass rod is $3,260 \mathrm{~m} / \mathrm{s}$ . If the density of brass is $8,470 \mathrm{~kg} / \mathrm{m}^{3}$ , then what is the elastic modulus of brass?

A) $9.00 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
B) $8.70 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
C) $9.80 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
D) $8.10 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$
E) $8.50 \times 10^{10} \mathrm{~N} / \mathrm{m}^{2}$

Question 9

A sound wave in brass has a displacement amplitude of $3.00 \mathrm{~mm}$ . The frequency of the sound wave $750 \mathrm{~Hz}$ and the speed is $2,813 \mathrm{~m} / \mathrm{s}$ . If the density of brass is $8.47 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}$ , then what is the pressure amplitude of the sound wave?

A) $3.37 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$
B) $4.70 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$
C) $4.17 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$
D) $5.38 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$
E) $5.10 \times 10^{8} \mathrm{~N} / \mathrm{m}^{2}$

Question 10

A sound wave in air has an intensity of $1.00 \times 10^{-3} \mathrm{~W} / \mathrm{m}^{2}$ . The density of air is $1.29 \mathrm{~kg} / \mathrm{m}^{3}$ and the speed of sound in air is $331 \mathrm{~m} / \mathrm{s}$ . The pressure amplitude of the sound wave is

A) $0.980 \mathrm{~N} / \mathrm{m}^{2}$ .
B) $0.850 \mathrm{~N} / \mathrm{m}^{2}$ .
C) $0.740 \mathrm{~N} / \mathrm{m}^{2}$ .
D) $0.821 \mathrm{~N} / \mathrm{m}^{2}$ .
E) $0.924 \mathrm{~N} / \mathrm{m}^{2}$ .

Question 11

A sound wave in water has an intensity of $1.00 \times 10^{-3} \mathrm{~W} / \mathrm{m}^{2}$ . The density of water is $1,000 \mathrm{~kg} / \mathrm{m}^{3}$ and the speed of sound in water is $1,482 \mathrm{~m} / \mathrm{s}$ . The pressure amplitude of the sound wave is

A) $42.5 \mathrm{~N} / \mathrm{m}^{2}$ .
B) $39.5 \mathrm{~N} / \mathrm{m}^{2}$ .
C) $49.5 \mathrm{~N} / \mathrm{m}^{2}$ .
D) $60.2 \mathrm{~N} / \mathrm{m}^{2}$ .
E) $54.4 \mathrm{~N} / \mathrm{m}^{2}$ .

Question 12

A sound wave in helium has an intensity of $1.00 \times 10^{-3} \mathrm{~W} / \mathrm{m}^{2}$ . The density of helium is $0.179 \mathrm{~kg} / \mathrm{m}^{3}$ and the speed of sound in helium is $965 \mathrm{~m} / \mathrm{s}$ . The pressure amplitude of the sound wave is

A) $0.276 \mathrm{~N} / \mathrm{m}^{2}$
B) $0.476 \mathrm{~N} / \mathrm{m}^{2}$ .
C) $0.345 \mathrm{~N} / \mathrm{m}^{2}$
D) $0.682 \mathrm{~N} / \mathrm{m}^{2}$ .
E) $0.588 \mathrm{~N} / \mathrm{m}^{2}$ .

Question 13

The sound of a jet engine is given as $120 \mathrm{~dB}$ . What is the intensity of the jet sound wave?

A) $0.6 \mathrm{~W} / \mathrm{m}^{2}$
B) $0.8 \mathrm{~W} / \mathrm{m}^{2}$
C) $1.0 \mathrm{~W} / \mathrm{m}^{2}$
D) $0.2 \mathrm{~W} / \mathrm{m}^{2}$
E) $0.4 \mathrm{~W} / \mathrm{m}^{2}$

Question 14

The sound of a bird singing is given as $5 \mathrm{~dB}$ . What is the intensity of the sound of a bird singing?

A) $4.25 \times 10^{-12} \mathrm{~W} / \mathrm{m}^{2}$
B) $3.16 \times 10^{-12} \mathrm{~W} / \mathrm{m}^{2}$
C) $2.98 \times 10^{-12} \mathrm{~W} / \mathrm{m}^{2}$
D) $1.95 \times 10^{-12} \mathrm{~W} / \mathrm{m}^{2}$
E) $2.04 \times 10^{-12} \mathrm{~W} / \mathrm{m}^{2}$

Question 15

The sound of a band is rated as $50 \mathrm{~dB}$ at a distance of $30.0 \mathrm{~m}$ . What is the sound intensity level of the band when one is $10.0 \mathrm{~m}$ from the band?

A) $52.9 \mathrm{~dB}$
B) $55.2 \mathrm{~dB}$
C) $50.1 \mathrm{~dB}$
D) $57.3 \mathrm{~dB}$
E) $59.5 \mathrm{~dB}$

Question 16

A string with a mass per length of $2.00 \mathrm{~g} / \mathrm{m}$ is stretched with a force of $150 \mathrm{~N}$ between two points that are $0.500 \mathrm{~m}$ apart. The fundamental frequency of the stretched string is in tune with the fundamental frequency of an organ pipe filled with air and open at both ends. The speed of sound in air at $0^{\circ} \mathrm{C}$ is $331 \mathrm{~m} / \mathrm{s}$ . What is the length of the organ pipe?

A) $50.2 \mathrm{~cm}$
B) $60.4 \mathrm{~cm}$
C) $57.5 \mathrm{~cm}$
D) $65.3 \mathrm{~cm}$
E) $55.2 \mathrm{~cm}$

Question 17

A string with a mass per length of $2.00 \mathrm{~g} / \mathrm{m}$ is stretched with a force of $120 \mathrm{~N}$ between two points that are $0.400 \mathrm{~m}$ apart. The fundamental frequency of the stretched string is in tune with the fundamental frequency of an organ pipe filled with air and open at both ends. The speed of sound in air at $0^{\circ} \mathrm{C}$ is $331 \mathrm{~m} / \mathrm{s}$ . What is the length of the organ pipe?

A) $54.1 \mathrm{~cm}$
B) $61.5 \mathrm{~cm}$
C) $66.8 \mathrm{~cm}$
D) $63.5 \mathrm{~cm}$
E) $59.0 \mathrm{~cm}$

Question 18

A string with a mass per length of $2.00 \mathrm{~g} / \mathrm{m}$ is stretched with a force of $150 \mathrm{~N}$ between two points that are $0.500 \mathrm{~m}$ apart. The frequency of the second mode of the stretched string is in tune with the fundamental frequency of an organ pipe filled with air and open at both ends. The speed of sound in air at $0^{\circ} \mathrm{C}$ is $331 \mathrm{~m} / \mathrm{s}$ . What is the length of the organ pipe?

A) $43.6 \mathrm{~cm}$
B) $40.1 \mathrm{~cm}$
C) $30.2 \mathrm{~cm}$
D) $35.6 \mathrm{~cm}$
E) $37.5 \mathrm{~cm}$

Question 19

A string with a mass per length of $2.00 \mathrm{~g} / \mathrm{m}$ is stretched with a force of $120 \mathrm{~N}$ between two points that are $0.400 \mathrm{~m}$ apart. The fundamental frequency of the stretched string is in tune with the frequency of the second mode of an organ pipe filled with air and open at both ends. The speed of sound in air at $0^{\circ} \mathrm{C}$ is $331 \mathrm{~m} / \mathrm{s}$ . What is the length of the organ pipe?

A) $95.0 \mathrm{~cm}$
B) $175 \mathrm{~cm}$
C) $225 \mathrm{~cm}$
D) $108 \mathrm{~cm}$
E) $125 \mathrm{~cm}$

Question 20

A string with a mass per length of $2.00 \mathrm{~g} / \mathrm{m}$ is stretched with a force of $150 \mathrm{~N}$ between two points that are $0.500 \mathrm{~m}$ apart. The fundamental frequency of the stretched string is in tune with the fundamental frequency of an organ pipe filled with air at $20^{\circ} \mathrm{C}$ and open at both ends. The speed of sound in air at $0^{\circ} \mathrm{C}$ is $331 \mathrm{~m} / \mathrm{s}$ . What is the length of the organ pipe?

A) $62.6 \mathrm{~cm}$
B) $50.2 \mathrm{~cm}$
C) $53.8 \mathrm{~cm}$
D) $59.3 \mathrm{~cm}$
E) $70.5 \mathrm{~cm}$

Question 21

A string with a mass per length of $2.00 \mathrm{~g} / \mathrm{m}$ is stretched with a force of $120 \mathrm{~N}$ between two points that are $0.400 \mathrm{~m}$ apart. The fundamental frequency of the stretched string is in tune with the frequency of the second mode of an organ pipe filled with air at $-20^{\circ} \mathrm{C}$ and open at both ends. The speed of sound in air at $0^{\circ} \mathrm{C}$ is $331 \mathrm{~m} / \mathrm{s}$ . What is the length of the organ pipe?

A) $150 \mathrm{~cm}$
B) $125 \mathrm{~cm}$
C) $75.0 \mathrm{~cm}$
D) $104 \mathrm{~cm}$
E) $175 \mathrm{~cm}$

Question 22

An ambulance is generating a siren sound at a frequency of 2,400 Hz. The speed of sound is $345.0 \mathrm{~m} / \mathrm{s}$ . The observer is traveling at a velocity of $24.00 \mathrm{~m} / \mathrm{s}$ toward the ambulance and the ambulance is traveling at a velocity of $24.00 \mathrm{~m} / \mathrm{s}$ toward the observer. What is the frequency of the siren perceived by the observer?

A) $2,100 \mathrm{~Hz}$
B) $2,430 \mathrm{~Hz}$
C) $2,759 \mathrm{~Hz}$
D) $2,550 \mathrm{~Hz}$
E) $2,250 \mathrm{~Hz}$

Question 23

An ambulance is generating a siren sound at a frequency of $2,400 \mathrm{~Hz}$ . The speed of sound is $345.0 \mathrm{~m} / \mathrm{s}$ . The observer is traveling at a velocity of $24.00 \mathrm{~m} / \mathrm{s}$ toward the ambulance and the ambulance is traveling at a velocity of $24.00 \mathrm{~m} / \mathrm{s}$ away the observer. What is the frequency of the siren perceived by the observer?

A) $2,424 \mathrm{~Hz}$
B) $2,352 \mathrm{~Hz}$
C) $2,376 \mathrm{~Hz}$
D) $2,448 \mathrm{~Hz}$
E) $2,400 \mathrm{~Hz}$

Question 24

An ambulance is generating a siren sound at a frequency of $2,400 \mathrm{~Hz}$ . The speed of sound is $345.0 \mathrm{~m} / \mathrm{s}$ . If the ambulance is traveling at a velocity of $24.00 \mathrm{~m} / \mathrm{s}$ toward the stationary observer, then what is the frequency of the siren perceived by the observer?

A) $2,525 \mathrm{~Hz}$
B) $2,480 \mathrm{~Hz}$
C) $2,500 \mathrm{~Hz}$
D) $2,540 \mathrm{~Hz}$
E) $2,579 \mathrm{~Hz}$

Question 25

An ambulance is generating a siren sound at a frequency of $2,400 \mathrm{~Hz}$ . The speed of sound is $345.0 \mathrm{~m} / \mathrm{s}$ . If the ambulance is traveling at a velocity of $24.00 \mathrm{~m} / \mathrm{s}$ away from the stationary observer, then what is the frequency of the siren perceived by the observer?

A) $2,244 \mathrm{~Hz}$
B) $2,266 \mathrm{~Hz}$
C) $2,306 \mathrm{~Hz}$
D) $2,375 \mathrm{~Hz}$
E) $2,210 \mathrm{~Hz}$

Question 26

An ambulance is generating a siren sound at a frequency of $2,400 \mathrm{~Hz}$ . The speed of sound is $345.0 \mathrm{~m} / \mathrm{s}$ . If the observer is traveling at a velocity of $24.00 \mathrm{~m} / \mathrm{s}$ toward the stationary ambulance, then what is the frequency of the siren perceived by the observer?

A) $2,508 \mathrm{~Hz}$
B) $2,640 \mathrm{~Hz}$
C) $2,567 \mathrm{~Hz}$
D) $2,520 \mathrm{~Hz}$
E) $2,475 \mathrm{~Hz}$

Question 27

An ambulance is generating a siren sound at a frequency of $2,400 \mathrm{~Hz}$ . The speed of sound is $345.0 \mathrm{~m} / \mathrm{s}$ . If the observer is traveling at a velocity of $24.00 \mathrm{~m} / \mathrm{s}$ away from the stationary ambulance, then what is the frequency of the siren perceived by the observer?

A) $2,366 \mathrm{~Hz}$
B) $2,233 \mathrm{~Hz}$
C) $2,275 \mathrm{~Hz}$
D) $2,305 \mathrm{~Hz}$
E) $2,375 \mathrm{~Hz}$

Question 28

An ambulance is generating a siren sound at a frequency of $2,400 \mathrm{~Hz}$ . The speed of sound is $345.0 \mathrm{~m} / \mathrm{s}$ . The observer is traveling at a velocity of $24.00 \mathrm{~m} / \mathrm{s}$ toward the ambulance and the ambulance is traveling at a velocity of $20.00 \mathrm{~m} / \mathrm{s}$ toward the observer. What is the frequency of the siren perceived by the observer?

A) $2,489 \mathrm{~Hz}$
B) $2,560 \mathrm{~Hz}$
C) $2,675 \mathrm{~Hz}$
D) $2,830 \mathrm{~Hz}$
E) $2,725 \mathrm{~Hz}$

Question 29

A guitar string with a tension of $150 \mathrm{~N}$ is played together with a tuning fork whose frequency is $256 \mathrm{~Hz}$ , and beats of $2 \mathrm{~Hz}$ are heard. Assuming the guitar string is higher in frequency than the tuning fork, to what new tension should the guitar string be adjusted for the string and tuning fork to have the same frequency?

A) $151 \mathrm{~N}$
B) $148 \mathrm{~N}$
C) $152 \mathrm{~N}$
D) $149 \mathrm{~N}$
E) The length of the string must be given in order to solve this problem.

Question 30

A $1024 \mathrm{~Hz}$ tuning fork is dangled at the end of a string such that its center of mass is $1.2 \mathrm{~m}$ below the point at which the other end of the string is attached to door frame, making a pendulum of sorts. The tuning fork may be treated as a point mass for the purposes of this problem. If the pendulum is brought to an amplitude of $22^{\circ}$ and released, what is the range of frequencies heard by an observer standing in the plane of the pendulum's motion? The speed of sound is $340 \mathrm{~m} / \mathrm{s}$ .

A) $1020 \mathrm{~Hz}$ to $1028 \mathrm{~Hz}$
B) $1010 \mathrm{~Hz}$ to $1038 \mathrm{~Hz}$
C) $1012 \mathrm{~Hz}$ to $1036 \mathrm{~Hz}$
D) $1015 \mathrm{~Hz}$ to $1033 \mathrm{~Hz}$

Question 31

A $1024 \mathrm{~Hz}$ tuning fork is dangled at the end of a string such that its center of mass is $1.2 \mathrm{~m}$ below the point at which the other end of the string is attached to door frame, making a pendulum of sorts. The tuning fork may be treated as a point mass for the purposes of this problem. The pendulum is brought to a maximum angle and released. If the range of frequencies heard by an observer standing in the plane of the pendulum's motion is $1020-1028 \mathrm{~Hz}$ , what is the angle to which the pendulum was raised? The speed of sound is $340 \mathrm{~m} / \mathrm{s}$ .

A) $17^{\circ}$
B) $4.3^{\circ}$
C) $18^{\circ}$
D) $46^{\circ}$
E) $22^{\circ}$

Question 32

A block holding a ringing tuning fork is attached to a wall by a spring. The block oscillates back and forth on a horizontal, frictionless surface, with amplitude $17 \mathrm{~cm}$ . The spring constant is $390 \mathrm{~N} / \mathrm{m}$ . An observer who is situated so that the block's direction of motion is either directly towards or away from him notes that the frequency he hears varies between 174 and $178 \mathrm{~Hz}$ . What is the mass of the tuning fork and block together? The speed of sound is $340 \mathrm{~m} / \mathrm{s}$ .

A) $2.9 \mathrm{~kg}$
B) $0.76 \mathrm{~kg}$
C) $4.4 \mathrm{~kg}$
D) $0.18 \mathrm{~kg}$

Question 33

A bat is flying toward a cave wall at $27.0 \mathrm{~m} / \mathrm{s}$ . What is the frequency of the reflected sound that it hears, assuming it emits sound at $52.0 \mathrm{kHz}$ ? The speed of sound is $341.5 \mathrm{~m} / \mathrm{s}$ .

A) $61.3 \mathrm{kHz}$
B) $56.1 \mathrm{kHz}$
C) $56.5 \mathrm{kHz}$
D) $60.9 \mathrm{kHz}$

Question 34

A bat is flying toward a cave wall. If it hears reflected sound of frequency $60.9 \mathrm{kHz}$ , what is its flying speed, assuming it emits sound at $52.0 \mathrm{kHz}$ ? The speed of sound is $341.5 \mathrm{~m} / \mathrm{s}$ .

A) $28.1 \mathrm{~m} / \mathrm{s}$
B) $26.9 \mathrm{~m} / \mathrm{s}$
C) $25.9 \mathrm{~m} / \mathrm{s}$
D) $49.9 \mathrm{~m} / \mathrm{s}$
E) $58.4 \mathrm{~m} / \mathrm{s}$