Deck 21: Mechanical Waves

Question 1

A string of mass m is under tension,and the speed of a wave in the string is v.What will be the speed of a wave in the string if the mass of the string is increased to 2m but with no change in the length or tension?

A)v/2
B)v/
C)v
D)2v
E)4v

Answer 1

B

Question 2

The intensity of the waves from a point source at a distance d from the source is I.At what distance from the sources is the intensity equal to 2I?

A)d/2
B)d/
C)d/4
D)d/8

Answer 2

B

Question 3

What characteristics of a sound wave are related to the "pitch" of a musical note? (There could be more than one correct choice.)

A)amplitude
B)wavelength
C)frequency
D)period

Answer 3

B,C,D

Question 4

What is the wavelength of the wave shown in the figure?

A)8 m.
B)4 m.
C)2 m.
D)1 m.
E)It cannot be determined from the given information.

Question 5

Seven seconds after a brilliant flash of lightning,thunder shakes the house.Approximately how far was the lightning strike from the house?

A)much closer than one kilometer
B)about one kilometer away
C)about two kilometers away
D)much farther away than two kilometers
E)It is impossible to say.

Question 6

What is the frequency of the wave shown in the figure?

A)0.5 Hz.
B)1 Hz.
C)2 Hz.
D)4 Hz.
E)It cannot be determined from the given information.

Question 7

The intensity of the waves from a point source at a distance d from the source is I.What is the intensity at a distance 2d from the source?

A)4I
B)2I
C)I/2
D)I/4
E)I/

Question 8

You double your distance from a sound source that is radiating equally in all directions.What happens to the intensity of the sound? It reduces to

A)one-half its original value.
B)one-fourth its original value.
C)one-sixteenth its original value.
D)none of the above

Question 9

Four waves are described by the following equations,where distances are measured in meters and times in seconds. I.y = 0.12 cos(3x - 21t)
II.y = 0.15 sin(6x + 42t)
III.y = 0.13 cos(6x + 21t)
IV.y = -0.23 sin(3x - 42t)
Which of these waves have the same speed?

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

Question 10

If a string fixed at both ends resonates in its fundamental mode with a frequency of 150 Hz,at which of the following frequencies will it not resonate? (There could be more than one correct choice.)

A)75 Hz
B)300 Hz
C)450 Hz
D)500 Hz
E)600 Hz

Question 11

Four waves are described by the following equations,where distances are measured in meters and times in seconds. I.y = 0.12 cos(3x - 21t)
II.y = 0.15 sin(6x + 42t)
III.y = 0.13 cos(6x + 21t)
IV.y = -0.23 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 12

A string of length L is under tension,and the speed of a wave in the string is v.What will be the speed of a wave in the string if the length is increased to 2L but with no change in the mass or tension?

A)v/2
B)v/
C)v
D)2v
E)4v

Question 13

A stretched string is observed to have four equal segments in a standing wave driven at a frequency of 480 Hz.What driving frequency will set up a standing wave with five equal segments?

A)600 Hz
B)360 Hz
C)240 Hz
D)120 Hz

Question 14

Sound A has a high pitch and sound B has a low pitch.Which of the following statements about these two sounds are correct? (There could be more than one correct choice.)

A)The wavelength of A is longer than the wavelength of B.
B)The period of A is shorter than the period of B.
C)The frequency of A is greater than the frequency of B.
D)Sound B travels faster than sound B through air.
E)The amplitude of A is larger than the amplitude of B.

Question 15

When a guitar is tuned to adjust it pitch,what is it that is changed?

A)The wavelength of the fundamental.
B)The frequency of the fundamental.
C)The amplitude of the fundamental.

Question 16

When a certain string is under tension T,the speed of a wave in the string is v.What will be the speed of a wave in the string if the tension is increased to 2T without changing the mass or length of the string?

A)v/2
B)v/
C)v
D)2v
E)4v

Question 17

Which one of the curves shown in the figure best represents the variation of wave speed v as a function of tension for transverse waves on a stretched string?

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

Question 18

A string fixed at both ends is vibrating in one of its harmonics.If we now increase only the frequency at which the string is vibrating,which of the following characteristics do we also increase? (There could be more than one correct choice.)

A)the speed of the traveling waves on the string
B)the period of the traveling waves on the string
C)the wavelength of the traveling waves on the string
D)the amplitude of the traveling waves on the string
E)none of the above

Question 19

If a guitar string has a fundamental frequency of 500 Hz,which one of the following frequencies can set the string into resonant vibration?

A)250 Hz
B)750 Hz
C)1500 Hz
D)1750 Hz

Question 20

Why does the intensity of waves from a small source decrease with the square of the distance from the source?

A)The waves run out of energy as they travel.
B)The waves spread out as they travel.
C)The medium through which the waves travel absorbs the energy of the waves.
D)The waves slow down as they travel away from the source.
E)The frequency of the waves decreases as they get farther from the source.

Question 21

A music tuner uses a 554-Hz C# tuning fork to tune the frequency of a musical instrument.If the tuner hears a beat frequency of 2 Hz,what is the frequency of the instrument?

A)It must be 556 Hz.
B)It must be 552 Hz.
C)It could be either 556 Hz or 552 Hz.
D)It could be either 553 Hz or 555 Hz.
E)It is neither 556 Hz or 552 Hz.

Question 22

Consider a pipe of length L that is open at one end and closed at the other end.What are the wavelengths of the three lowest-pitch tones produced by this pipe?

A)4L, 2L, L
B)2L, L, L/2
C)2L, L, 2 L/3
D)4L, 4L/3, 4L/5

Question 23

Two strings both vibrate at exactly 819 Hz.The tension in one of them is then increased slightly.As a result,six beats per second are heard when both strings vibrate.What is the new frequency of the string that was tightened?

A)825 Hz
B)813 Hz
C)822 Hz
D)816 Hz

Question 24

An organ pipe of length L that is open at one end resonates in its third harmonic with a wavelength of 2L/3.Is the other end of the pipe closed or open?

A)closed
B)open
C)We cannot tell from the information provided.

Question 25

In many cartoon shows,a character runs off a cliff,realizes his predicament,and lets out a scream.He continues to scream as he falls.If the physical situation is portrayed correctly,from the vantage point of an observer at the foot of the cliff,the pitch of the scream as he falls should be

A)higher than the original pitch and constant.
B)higher than the original pitch and increasing as he falls.
C)lower than the original pitch and constant.
D)lower than the original pitch and decreasing as he falls.
E)It is impossible to predict.

Question 26

As you are moving very quickly toward a speaker emitting a pure tone,which characteristics of the sound get larger? (There may be more than one correct choice.)

A)frequency
B)amplitude
C)wavelength
D)period
E)loudness

Question 27

A tsunami,an ocean wave generated by an earthquake,propagates along the open ocean at 700 km/hr and has a wavelength of 750 km.What is the frequency of the waves in such a tsunami?

A)0.93 Hz
B)0.00026 Hz
C)1.1 Hz
D)6.8 Hz
E)0.15 Hz

Question 28

Two tuning forks have frequencies of 440 and 522 Hz.What is the beat frequency if both are sounding simultaneously?

A)962 Hz
B)481 Hz
C)82 Hz
D)55 Hz
E)41 Hz

Question 29

Two pure tones are sounded together and a particular beat frequency is heard.What happens to the beat frequency if the frequency of one of the tones is increased?

A)It increases.
B)It decreases.
C)It does not change.
D)It could either increase or decrease.

Question 30

In a resonating pipe that is open at both ends,there

A)are displacement nodes at each end.
B)are displacement antinodes at each end.
C)is a displacement node at one end and a displacement antinode at the other end.
D)None of the above choices are correct.

Question 31

An pipe of length L that is open at both ends is resonating at its fundamental frequency.Which statement about the sound is correct?

A)The wavelength is 2L and there is a displacement node at the pipe's midpoint.
B)The wavelength is 2L and there is a displacement antinode at the pipe's midpoint.
C)The wavelength is L and there is a displacement node at the pipe's midpoint.
D)The wavelength is L and there is a displacement antinode at the pipe's midpoint.

Question 32

Consider the standing wave on a guitar string and the sound wave generated by the string as a result of this vibration.What do these two waves have in common? (There may be more than one correct choice.)

A)They have the same wavelength.
B)They have the same speed.
C)They have the same frequency.
D)They have the same amplitude.
E)They have the same period.

Question 33

The lowest tone to resonate in pipe of length L that is open at both ends is 200 Hz.Which one of the following frequencies will not resonate in the same pipe?

A)200 Hz
B)400 Hz
C)600 Hz
D)800 Hz
E)900 Hz

Question 34

In a resonating pipe that is open at one end and closed at the other end,there

A)are displacement nodes at each end.
B)are displacement antinodes at each end.
C)is a displacement node at the open end and a displacement antinode at the closed end.
D)is a displacement node at the closed end and a displacement antinode at the open end.

Question 35

A person stands between two speakers driven by the same source.Each speaker produces a tone with a frequency of 200 Hz on a day when the speed of sound is 330 m/s.The person is 1.65 m from one speaker and 4.95 m from the other.What type of interference does the person perceive?

A)constructive
B)destructive
C)both constructive and destructive
D)neither constructive nor destructive

Question 36

Suppose that a sound source is emitting waves uniformly in all directions.If you move to a point twice as far away from the source,the frequency of the sound will be

A)unchanged.
B)half as great.
C)one-fourth as great.
D)twice as great.

Question 37

The lowest tone to resonate in a pipe of length L that is closed at one end but open at the other end is 200 Hz.Which one of the following frequencies will not resonate in that pipe?

A)200 Hz
B)400 Hz
C)600 Hz
D)1000 Hz
E)1400 Hz

Question 38

Consider a pipe of length L that is open at both ends.What are the wavelengths of the three lowest-pitch tones produced by this pipe?

A)4L, 2L, L
B)2L, L, L/2
C)2L, L, 2L/3
D)4L, 4L/3, 4L/5

Question 39

A fisherman fishing from a pier observes that the float on his line bobs up and down,taking 2.4 s to move from its highest point to its lowest point.He also estimates that the distance between adjacent wave crests is 48 m.What is the speed of the waves going past the pier?

A)1.0 m/s
B)20 m/s
C)10 m/s
D)5.0 m/s
E)120 m/s

Question 40

In many cartoon shows,a character runs off a cliff,realizes his predicament,and lets out a scream.He continues to scream as he falls.If the physical situation is portrayed correctly,from the vantage point of an observer at the top of the cliff leaning over the edge,the pitch of the scream as he falls should be

A)higher than the original pitch and constant.
B)higher than the original pitch and increasing as he falls.
C)lower than the original pitch and constant.
D)lower than the original pitch and decreasing as he falls.
E)It is impossible to predict.

Question 41

A 2.31-kg rope is stretched between supports that are 10.4 m apart,and has a tension in it of 49.2 N.If one end of the rope is slightly tweaked,how long will it take for the resulting disturbance to reach the other end?

A)0.699 s
B)0.720 s
C)0.664 s
D)0.615 s

Question 42

A 90-gram wire that is 1.0 m long is under tension.When a transverse wave of frequency 890 Hz travels down the wire,its wavelength is 0.10 m and its amplitude is 6.5 mm.What is the tension in the wire?

A)710 N
B)820 N
C)930 N
D)1000 N
E)1100 N

Question 43

Crests of an ocean wave pass a pier every If the waves are moving at what is the wavelength of the ocean waves?

A)56 m
B)28 m
C)64 m
D)48 m

Question 44

A rope with a total mass of 25.0 kg is tied to a tree on one side of a 125-m wide ravine.You are pulling on the other end of the rope with a force of 415 N.If you pluck the rope at your end,how long will it take the pulse to travel across the ravine to the tree?

Question 45

The speed of sound in steel is 5000 m/s.What is the wavelength of a sound wave of frequency in steel?

A)7.58 m
B)2.41 m
C)1.21 m
D)0.829 m
E)0.132 m

Question 46

An earthquake generates three kinds of waves: surface waves (L-waves),which are the slowest and weakest,shear (S)waves,which are transverse waves and carry most of the energy,and pressure (P)waves,which are longitudinal waves and are the fastest.The speed of P waves is approximately 7 km/s,and that of S waves is about 4 km/s.People do not generally feel the P waves,but animals seem to be sensitive to them.If a person reports that her dog started barking 20 seconds "before the earthquake," then approximately how far was the origin of the earthquake?

A)100 km
B)200 km
C)300 km
D)400 km
E)500 km

Question 47

A 10-gram wire that is 6.0 m long is under tension.When a transverse wave of frequency 280 Hz travels along the wire,its wavelength is 0.60 m,and its amplitude is 8.4 mm.How much time does it take for a crest of the transverse wave to travel the length of the wire?

A)36 ms
B)31 ms
C)40 ms
D)44 ms
E)49 ms

Question 48

A crane lifts a 2500-kg beam using a steel cable whose mass per unit length is 0.650 kg/m.What is the speed of transverse waves on this cable if the upward acceleration of the beam is a steady 3.00 m/s²?

A)194 m/s
B)578 m/s
C)1220 m/s
D)1880 m/s
E)222 m/s

Question 49

The density of aluminum is 2700 kg/m³.If transverse waves travel at in an aluminum wire of diameter what is the tension on the wire?

A)65 N
B)39 N
C)52 N
D)78 N

Question 50

The figure shows a "snapshot" of a wave at a given instant of time.The frequency of this wave is 120 Hz.What are the (a)amplitude,(b)wavelength,and (c)speed of this wave?

Question 51

A wave whose wavelength is 0.500 m is traveling down a 500-m long wire whose total mass is 25 kg and is under a tension of 2000 N.
(a)What is the speed of the wave on the wire?
(b)Find the frequency of this wave.

Question 52

Two steel wires are stretched with the same tension.The first wire has a diameter of 0.610 mm and the second wire has a diameter of 0.910 mm.If the speed of waves traveling along the first wire is 54.0 m/s,what is the speed of waves traveling along the second wire?

A)24.9 m/s
B)27.2 m/s
C)36.2 m/s
D)81.0 m/s
E)100 m/s

Question 53

A wire that is 1.0 m long with a mass of 90 g is under a tension of 710 N.When a transverse wave travels on the wire,its wavelength is 0.10 m and its amplitude is 6.5 mm.What is the frequency of this wave?

A)890 Hz
B)920 Hz
C)1000 Hz
D)1200 Hz
E)1500 Hz

Question 54

A 1.1-kg uniform bar of metal is 0.40 m long and has a diameter of 2.0 cm.When someone bangs one end of this bar,a 1.5 MHz shock wave is travels along the length of the bar and reaches the other end in 0.12 ms.What is the wavelength of the shock wave in the metal?

A)2.2 mm
B)2.6 mm
C)3.0 mm
D)3.4 mm
E)3.8 mm

Question 55

A piano wire of linear mass density 0.0050 kg/m is under a tension of 1350 N.What is the wave speed in this wire?

A)130 m/s
B)260 m/s
C)520 m/s
D)1040 m/s

Question 56

A 15-m rope is pulled taut with a tension of 140 N.It takes 0.545 s for a wave to propagate along the rope.What is the mass of the rope?

A)1.7 kg
B)2.1 kg
C)2.8 kg
D)5.1 kg
E)3.2 kg

Question 57

A crane lifts a 2500-kg beam at a steady rate of 15 cm/s using a steel cable whose mass per unit length is 0.65 kg/m.What is the speed of transverse waves on this cable?

A)230 m/s
B)580 m/s
C)1200 m/s
D)1900 m/s
E)190 m/s

Question 58

What is the frequency of a pressure wave of wavelength 2.5 m that is traveling at 1400 m/s?

A)178 Hz
B)1.78 kHz
C)560 Hz
D)5.6 kHz

Question 59

If a wave has a speed of 362 m/s and a period of 4.17 ms,what is its wavelength?

A)1510 m
B)1.51 m
C)86.8 m
D)86,800 m
E)0.0115 m

Question 60

Transverse waves travel at in a string that is subjected to a tension of If the string is long,what is its mass?

A)0.515 kg
B)0.216 kg
C)0.366 kg
D)0.597 kg

Question 61

One of the harmonics of a string fixed at both ends has a frequency of 52.2 Hz and the next higher harmonic has a frequency of 60.9 Hz.What is the fundamental frequency of the string?

A)26.1 Hz
B)8.7 Hz
C)4.35 Hz
D)30.4 Hz
E)17.4 Hz

Question 62

The speed of propagation of a transverse wave on a 2.0-m long string fixed at both ends is 200 m/s.Which one of the following is not a resonant frequency of this string?

A)25 Hz
B)50 Hz
C)100 Hz
D)200 Hz

Question 63

A 0.588-m string is tightly clamped at both ends.If the lowest standing wave frequency of the string is how fast do waves travel on this string?

A)383 m/s
B)475 m/s
C)582 m/s
D)724 m/s

Question 64

A guitar string 0.65 m long has a tension of 61 N and a mass per unit length of 3.0 g/m.
(a)What is the speed of waves on the string when it is plucked?
(b)What is the string's fundamental frequency of vibration when plucked?
(c)At what other frequencies will this string vibrate?

Question 65

What is the frequency of the fundamental mode of vibration of a steel piano wire stretched to a tension of 440 N? The wire is 0.600 m long and has a mass of 5.60 g.

A)517 Hz
B)234 Hz
C)181 Hz
D)312 Hz
E)366 Hz

Question 66

The vertical displacement y(x,t)of a horizontal string aligned along the x-axis is given by the equation y(x,t)= (6.00 mm)cos[(3.25 m^-1)x - (7.22 s^-1)t].What are the (a)speed and (b)amplitude of this wave?

Question 67

Find the speed of an ocean wave whose displacement is given by the equation where x and y are in meters and t is in seconds.

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

Question 68

A 4.0-g string is 0.39 m long and is under tension.The string vibrates at 600 Hz in its third harmonic.What is the tension in this string?

A)250 N
B)200 N
C)160 N
D)290 N
E)340 N

Question 69

Standing waves of frequency 17 Hz are produced on a string that has a mass per unit length of To what tension must the string be stretched between two supports if adjacent nodes in the standing wave are to be 0.87 m apart?

Question 70

A string that is 2.0 meters long is fixed at both ends and tightened until the wave speed is What is the frequency of the standing wave shown in the figure?

A)27 Hz
B)54 Hz
C)81 Hz
D)110 Hz

Question 71

The vertical displacement y(x,t)of a horizontal string aligned along the x-axis is given by the equation y(x,t)= (6.00 mm)cos[(3.25 m^-1)x - (7.22 s^-1)t].What are the (a)wavelength and (b)period of this wave?

Question 72

A standing wave is oscillating at 950 Hz on a string,as shown in the figure.What is the wave speed?

A)380 m/s
B)570 m/s
C)290 m/s
D)190 m/s

Question 73

A 25-g string is stretched with a tension of 43 N between two fixed points 12 m apart.What is the frequency of the second harmonic?

A)6.0 Hz
B)12 Hz
C)18 Hz
D)24 Hz
E)36 Hz

Question 74

A string of length 2.5 m is fixed at both ends.When the string vibrates at a frequency of 85 Hz,a standing wave with five loops is formed.
(a)Determine the distance between two adjacent nodes.
(b)Determine the wavelength of the waves that travel on the string.
(c)Determine the speed of traveling waves on this string.
(d)Determine the fundamental frequency of this string.

Question 75

What is the wave speed in a brass wire with a radius of 0.500 mm stretched with a tension of 125 N? The density of brass is 8.60 × 10³ kg/m³.

A)0.121 m/s
B)100 m/s
C)136 m/s
D)500 m/s
E)68.8 m/s

Question 76

What are the wavelength (in meters)and frequency (in hertz)of a wave whose displacement is given by the equation y = 0.5 sin(0.20x + 120t),where x and y are in meters and t is in seconds?

A)10 m, 0.50 Hz
B)5.0 m, 10 Hz
C)19 m, 120 Hz
D)31 m, 19 Hz
E)0.20 m, 120 Hz

Question 77

Find the first three harmonics of a string of linear mass density 2.00 g/m and length 0.600 m when the tension in it is 50.0 N.

A)132 Hz, 264 Hz, 395 Hz
B)66 Hz, 132 Hz, 198 Hz
C)264 Hz, 528 Hz, 792 Hz
D)none of the above

Question 78

A guitar-like stringed instrument has a string that is 16 cm long.It sounds the musical note A (440 Hz)when played without fingering.By what distance should you shorten it to play the note C (523 Hz)?

A)2.5 cm
B)1.7 cm
C)3.4 cm
D)4.2 cm

Question 79

A 4.0-g string is 0.36 m long and is under tension.The string vibrates at 500 Hz in its third harmonic.What is the wavelength of the standing wave in the string?

A)0.24 m
B)0.36 m
C)0.54 m
D)0.72 m
E)0.90 m

Question 80

A string of linear density 1.5 g/m is under a tension of 20 N.What should be its length if its fundamental resonance frequency is 220 Hz?

A)0.26 m
B)0.96 m
C)1.1 m
D)1.2 m