Deck 16: Traveling Waves

Question 1

The figure shows the displacement y of a wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position.Determine the frequency of the wave.

A)4.0 Hz
B)0.50 Hz
C)3.0 Hz
D)0.33 Hz
E)0.25 Hz

Answer 1

0.25 Hz

Question 2

Four traveling waves are described by the following equations,where all quantities are measured in SI units and y represents the displacement. I: y = 0.12 cos(3x + 2t)
II: y = 0.15 sin(6x - 3t)
III: y = 0.23 cos(3x + 6t)
IV: y = -0.29 sin(1.5x - t)
Which of these waves have the same speed?

A)I and III
B)I and IV
C)II and III
D)I and II
E)III and IV

Answer 2

I and IV

Question 3

The vertical displacement y(x,t)of a string stretched along the horizontal x-axis is given by y(x,t)= (6.00 mm)cos[(3.25 m^-1)x - (7.22 rad/s)t].
(a)What is the minimum time for each complete cycle of the wave?
(b)What is the distance between adjacent crests of the wave?
(c)How fast does this wave travel?

Answer 3

(a)0.870 s (b)1.93 m (c)2.22 m/s

Question 4

The figure shows the displacement y of a traveling wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position.Determine the wavelength of the wave.

A)2.0 cm
B)3.0 m
C)2.0 m
D)4.0 m
E)1.5 m

Question 5

What characteristic of sound determines the "pitch" of a musical note?

A)amplitude
B)wavelength
C)frequency
D)phase
E)intensity

Question 6

When a weight W is hanging from a light vertical string,the speed of pulses on the string is V.If a second weight W is added without stretching the string,the speed of pulses on this string will now become

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

Question 7

Four traveling waves are described by the following equations,where all quantities are measured in SI units and y represents the displacement. I: y = 0.12 cos(3x - 21t)
II: y = 0.15 sin(6x + 42t)
III: y = 0.13 cos(6x + 21t)
IV: y = -0.27 sin(3x - 42t)
Which of these waves have the same period?

A)I and III,and also II and IV
B)I and IV,and also II and III
C)I and II,and also III and IV
D)All of them have the same period.
E)They all have different periods.

Question 8

The figure shows the displacement y of a traveling wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position.How fast is the wave traveling?

A)3.0 m/s
B)0.75 m/s
C)0.66 m/s
D)1.5 m/s
E)2.0 m/s

Question 9

A plane flies toward a stationary siren at 1/4 the speed of sound.Then the plane stands still on the ground and the siren is driven toward it at 1/4 the speed of sound.In both cases,a person sitting in the plane will hear the same frequency of sound from the siren.

Question 10

A stationary siren emits sound of frequency 1000 Hz and wavelength 0.343 m.An observer who is moving toward the siren will measure a frequency f and wavelength λ for this sound such that

A)f > 1000 Hz and λ > 0.343 m.
B)f > 1000 Hz and λ = 0.343 m.
C)f > 1000 Hz and λ < 0.343 m.
D)f = 1000 Hz and λ < 0.343 m.

Question 11

Ocean tides are waves that have a period of 12 hours,an amplitude (in some places)of 1.50 m,and a speed of 750 km/hr.What is the distance between adjacent crests of these waves?

A)9000 km
B)32,400 km
C)9000 m
D)32,400 m
E)2500 m

Question 12

You are generating traveling waves on a stretched string by wiggling one end.If you suddenly begin to wiggle more rapidly without appreciably affecting the tension,you will cause the waves to move down the string

A)faster than before.
B)slower than before.
C)at the same speed as before.

Question 13

A transverse wave traveling along a string transports energy at a rate r.If we want to double this rate,we could

A)increase the amplitude of the wave by a factor of 8.
B)increase the amplitude of the wave by a factor of 4.
C)increase the amplitude of the wave by a factor of 2.
D)increase the amplitude by a factor of .
E)increase the amplitude by a factor of .

Question 14

Find the speed of an ocean wave whose vertical displacement y as a function of time t is given by y(x,t)= 3.7 cos(2.2x - 5.6t),where all quantities are in SI units.

A)2.5 m/s
B)1.9 m/s
C)3.5 m/s
D)4.5 m/s

Question 15

For the wave shown in the figure,the frequency is

A)0.5 Hz.
B)1 Hz.
C)2 Hz.
D)4 Hz.
E)unable to be determined from the given information.

Question 16

In the figure,which of the curves best represents the variation of wave speed as a function of tension for transverse waves on a stretched string?

A)A
B)B
C)C
D)D
E)E

Question 17

A transverse wave is traveling on a string stretched along the horizontal x-axis.The equation for the vertical displacement y of the string is given by y = 0.0020 cos[π(15x - 52t)],where all quantities are in SI units.The maximum speed of a particle of the string is closest to

A)0.33 m/s.
B)0.43 m/s.
C)0.53 m/s.
D)0.64 m/s.
E)0.74 m/s.

Question 18

Which one of the following statements is true?

A)Both the intensity level (in dB)and the sound intensity can never be negative.
B)The intensity level (in dB)obeys an inverse-square distance law,but the sound intensity does not.
C)Both intensity level (in dB)and sound intensity obey inverse-square distance laws.
D)The sound intensity can never be negative,but the intensity level (in dB)can be negative.
E)Both the intensity level (in dB)and the sound intensity can be negative.

Question 19

For the wave shown in the figure,the wavelength is

A)8 m.
B)4 m.
C)2 m.
D)1 m.
E)unable to be determined from the given information.

Question 20

When a rocket is traveling toward a mountain at 100 m/s,the sound waves from this rocket's engine approach the mountain at speed V.If the rocket doubles its speed to 200 m/s,the sound waves from the engine will now approach the mountain at speed

A)4V.
B)2V.
C) V.
D)V.

Question 21

The density of aluminum is 2700 kg/m³.If transverse waves propagate at in a aluminum wire,what is the tension on the wire?

A)52 N
B)31 N
C)42 N
D)62 N

Question 22

A howler monkey is the loudest land animal and,under some circumstances,can be heard up to a distance of 5.0 km.Assume the acoustic output of a howler to be uniform in all directions and that the threshold of hearing is 1.0 × 10^-12 W/m².The acoustic power emitted by the howler is closest to

A)0.31 mW.
B)0.11 mW.
C)1.1 mW.
D)3.2 mW.
E)11 mW.

Question 23

A certain crying baby emits sound with an intensity of 8.0 × 10^-8 W/m².What is the intensity level due to a set of five such crying babies,all crying with the same intensity? You can neglect any absorption,reflection,or interference of the sound.The lowest detectable intensity is 1.0 × 10^-12 W/m².

A)79 dB
B)69 dB
C)56 dB
D)49 dB
E)36 dB

Question 24

Waves travel along a 100-m length of string which has a mass of 55 g and is held taut with a tension of 75 N.What is the speed of the waves?

A)3700 m/s
B)370 m/s
C)37 m/s
D)0.37 m/s
E)3.7 m/s

Question 25

A pipe that is 20.0 m long and 10.0 cm in diameter contains olive oil.The density of the olive oil is 890 kg/m³ and the bulk modulus is 1.3 × 10⁹ Pa.A 3.4-Hz longitudinal wave is transmitted in the oil.How many milliseconds does it take for the wave to travel the length of the pipe in the oil?

A)17 ms
B)15 ms
C)14 ms
D)13 ms
E)12 ms

Question 26

Two people are talking at a distance of 3.0 m from where you are and you measure the sound intensity as 1.1 × 10^-7 W/m².Another student is 4.0 m away from the talkers.What sound intensity does the other student measure? Assume that the sound spreads out uniformly and undergoes no significant reflections or absorption.

A)6.2 × 10^-8 W/m²
B)1.5 × 10^-7 W/m²
C)8.3 × 10^-8 W/m²
D)7.8 × 10^-7 W/m²
E)2.5 × 10^-8 W/m²

Question 27

An enclosed chamber with sound absorbing walls has a 2.0 m × 1.0 m opening for an outside window.A loudspeaker is located outdoors,84 m away and facing the window.The intensity level of the sound entering the window space from the loudspeaker is 56 dB.Assume the acoustic output of the loudspeaker is uniform in all directions and that acoustic energy incident upon the ground is completely absorbed and therefore is not reflected into the window.The threshold of hearing is 1.0 × 10^-12 W/m².The acoustic power output of the loudspeaker is closest to

A)0.035 W.
B)0.070 W.
C)0.18 W.
D)0.35 W.
E)0.70 W.

Question 28

A sound source emits 20.0 W of acoustical power spread equally in all directions.The threshold of hearing is 1.0 × 10^-12 W/m².What is the sound intensity level 30.0 m from the source?

A)92.5 dB
B)81.5 dB
C)1.77 × 10^-3 dB
D)1.77 × 10^-3 W
E)-27.5 dB

Question 29

Observer A is 3.0 m from a tiny light bulb and observer B is 12.0 m from the same bulb.Assume that the light spreads out uniformly and undergoes no significant reflections or absorption.If observer B sees a light of intensity I,the light intensity that A sees is

A)I.
B)9I.
C)16I.
D)36I.
E)144I.

Question 30

The sound level at 1.0 m from a certain talking person talking is 60 dB.You are surrounded by five such people,all 1.0 m from you and all talking equally loud at the same time.The threshold of hearing is 1.0 × 10^-12 W/m².What sound level are you being exposed to? You can neglect any absorption,reflection,or interference of the sound.The threshold of hearing is 1.0 × 10^-12 W/m².

A)300 dB
B)60 dB
C)74 dB
D)67 dB
E)81 dB

Question 31

Calculate the light intensity 1.51 m from a light bulb that emits 100 W of visible light,assuming that the light radiates uniformly in all directions.

A)3.49 W/m²
B)4.01 W/m²
C)43.9 W/m²
D)50.5 W/m²

Question 32

A 8.0-m long wire with a mass of 10 g is under tension.A transverse wave for which the frequency is 570 Hz,the wavelength is 0.10 m,and the amplitude is 3.7 mm is propagating on the wire.The maximum transverse acceleration of a point on a wire is closest to

A)47,000 m/s².
B)41,000 m/s².
C)35,000 m/s².
D)29,000 m/s².
E)53,000 m/s².

Question 33

You and your surfing buddy are waiting to catch a wave a few hundred meters off the beach.The waves are conveniently sinusoidal,and you notice that when you're on the top of one wave and moving toward your friend,she is exactly halfway between you and the trough of the wave.1.50 seconds later,your friend is at the top of the wave.You estimate the horizontal distance between you and your friend at 8.00 m.
(a)What is the frequency of the waves?
(b)Find the speed of the waves.

Question 34

An enclosed chamber with sound absorbing walls has a 2.0 m × 1.0 m opening for an outside window.A loudspeaker is located outdoors,78 m away and facing the window.The intensity level of the sound entering the window space from the loudspeaker is 79 dB.Assume the acoustic output of the loudspeaker is uniform in all directions and that the acoustic energy incident upon the ground is completely absorbed and therefore is not reflected into the window.The threshold of hearing is 1.0 × 10^-12 W/m².The acoustic power entering through the window space is closest to

A)160 µW.
B)79 µW.
C)320 µW.
D)790 µW.
E)1600 µW.

Question 35

The howler monkey is the loudest land animal and,under some circumstances,can be heard up to a distance of 8.9 km.Assume the acoustic output of a howler to be uniform in all directions and that the threshold of hearing is 1.0 × 10^-12 W/m².A juvenile howler monkey has an acoustic output of What is the ratio of the acoustic intensity produced by the juvenile howler to the reference intensity I₀,at a distance of 210 m?

A)110
B)230
C)76
D)170
E)300

Question 36

A 6.00-m long rope is under a tension of 600 N.Waves travel along this rope at 40.0 m/s.What is the mass of the rope?

A)1.00 kg
B)1.25 kg
C)2.25 kg
D)2.50 kg
E)1.12 kg

Question 37

A tiny vibrating source sends waves uniformly in all directions.An area of 3.25 cm² on a sphere of radius 2.50 m centered on the source receives energy at a rate of 4.20 J/s.
(a)What is the intensity of the waves at 2.50 m from the source and at 10.0 m from the source?
(b)At what rate is energy leaving the vibrating source of the waves?

Question 38

The intensity of sunlight falling on the earth is about 1.4 kW/m² (before any gets absorbed by our atmosphere).At what rate does the sun emit light energy? (The earth-sun distance = 1.5 × 10⁸ km and the earth's radius = 6.4 × 10³ km.)

A)4.0 × 10²⁶ W
B)3.2 × 10²² W
C)7.2 × 10¹⁴ W
D)7.6 × 10⁸ W

Question 39

A heavy stone of mass m is hung from the ceiling by a thin 8.25-g wire that is 65.0 cm long.When you gently pluck the upper end of the wire,a pulse travels down the wire and returns 7.84 ms later,having reflected off the lower end.The stone is heavy enough to prevent the lower end of the wire from moving.What is the mass m of the stone?

A)8.90 kg
B)23.1 kg
C)35.6 kg
D)227 kg
E)349 kg

Question 40

A 6.0-m wire with a mass of 50 g,is under tension.A transverse wave,for which the frequency is 810 Hz,the wavelength is 0.40 m,and the amplitude is 4.0 mm,is propagating on the wire.The time for a crest of this wave to travel the length of the wire is closest to

A)19 ms.
B)16 ms.
C)21 ms.
D)23 ms.
E)25 ms.

Question 41

A factory siren indicating the end of a shift has a frequency of 90.0 Hz.The speed of sound is 343 m/s.
(a)What frequency is perceived by the occupant of a car traveling towards the factory at
25.0 m/s?
(b)What frequency is perceived by the occupant of a car traveling away from the factory at
30.0 m/s?

Question 42

The speed of sound in the air inside a 0.640-m long gas column is 340 m/s.What is the fundamental resonant frequency of this air column if it is
(a)open at one end and closed at the other end?
(b)open at both ends?

Question 43

A carousel that is 5.00 m in radius has a pair of 600-Hz sirens mounted on posts at opposite ends of a diameter.The carousel rotates with an angular velocity of 0.800 rad/s.A stationary listener is located at a distance from the carousel.The speed of sound is 350 m/s.The maximum beat frequency of the sirens at the position of the listener is closest to

A)6 Hz.
B)8 Hz.
C)10 Hz.
D)12 Hz.
E)14 Hz.

Question 44

A bat emits a sound at a frequency of 30.0 kHz as it approaches a wall.The bat detects beats such that the frequency of the echo is 900 Hz higher than the frequency the bat is emitting.The speed of sound in air is 340 m/s.The speed of the bat is closest to

A)20.0 m/s.
B)530 m/s.
C)10.0 m/s.
D)30.0 m/s.
E)5.02 m/s.

Question 45

As you stand by the side of the road,a car approaches you at a constant speed,sounding its horn,and you hear a frequency of 80.0 Hz.After the car goes by,you hear a frequency of 60.0 Hz.What is the speed of the car? The speed of sound in the air is 343 m/s.

A)64.0 m/s
B)49.0 m/s
C)16.0 m/s
D)36.0 m/s
E)25.0 m/s

Question 46

If the intensity level at distance d of one trombone is 70 dB,what is the intensity level of 76 identical trombones,all at distance d?

A)146 dB
B)89 dB
C)5320 dB
D)76 dB
E)82 dB

Question 47

You are driving along a highway at 35.0 m/s when you hear the siren of a police car approaching you from behind and you perceive the frequency as 1310 Hz.You are relieved that he is in pursuit of a different speeder when he continues past you,but now you perceive the frequency as 1240 Hz.What is the frequency of the siren in the police car? The speed of sound in air is 343 m/s.

A)1300 Hz
B)1320 Hz
C)1270 Hz
D)1360 Hz
E)1370 Hz

Question 48

You are driving along a highway at 35.0 m/s when you hear the siren of a police car approaching you from behind and you perceive the frequency as 1370 Hz.You are relieved that he is in pursuit of a different speeder when he continues past you,but now you perceive the frequency as 1330 Hz.What is the speed of the police car? The speed of sound in air is 343 m/s.

A)38.4 m/s
B)30.0 m/s
C)39.2 m/s
D)40.0 m/s
E)41.7 m/s

Question 49

The intensity level of a "Super-Silent" power lawn mower at a distance of 1.0 m is 100 dB.You wake up one morning to find that four of your neighbors are all mowing their lawns using identical "Super-Silent" mowers.When they are each 20 m from your open bedroom window,what is the intensity level of the sound in your bedroom? You can neglect any absorption,reflection,or interference of the sound.The lowest detectable intensity is 1.0 × 10^-12 W/m².

A)80 dB
B)104 dB
C)400 dB
D)50 dB
E)40 dB

Question 50

At a distance of 2.00 m from a point source of sound,the intensity level is 80.0 dB.What will be the intensity level at a distance of 4.00 m from this source? The lowest detectable intensity is 1.0 × 10^-12 W/m².

A)77.0 dB
B)74.0 dB
C)60.0 dB
D)40.0 dB
E)20.0 dB

Question 51

A boy on a bicycle approaches a brick wall as he sounds his horn at a frequency 400.00 Hz.The sound he hears reflected back from the wall is at a frequency 408.00 Hz.At what is the speed is the boy riding his bicycle toward the wall? Assume the speed of sound in air is 340 m/s.

A)3.68 m/s
B)333 m/s
C)6.67 m/s
D)6.80 m/s
E)3.37 m/s