Deck 15: Traveling Waves and Sound

Question 1

A uniform bar of metal,0.40 m long,with a diameter of 2.0 cm,has a mass of 1.1 kg. A 1.5 MHz longitudinal wave is propagated along the length of the bar.A wave compression traverses the length of the bar in 0.12 ms.The wavelength of the longitudinal wave in the metal,in mm,is closest to:

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

Answer 1

2.2

Question 2

A string,30 cm long and having a mass of 45 g,is attached to a 810 Hz vibrator at one end.The other end of the string is fixed and the string is kept under tension.The vibrator produces a transverse wave in the string,whose amplitude is 7.0 mm,and that propagates with a velocity of 76 m/s.The energy of the wave is absorbed at the fixed end.In this situation,the tension in the string,in SI units,is closest to:

A)870
B)830
C)900
D)940
E)970

Answer 2

870

Question 3

Find the displacement of a simple harmonic wave of amplitude 6.44 m at t = 0.71 s.Assume that the wave number is 2.34 m^-1,the angular frequency is 2.88 rad/s,and that the wave is propagating in the +x direction at x = 1.21 m.

A)4.55 m
B)1.05 m
C)3.54 m
D)2.25 m

Answer 3

4.55 m

Question 4

If a wave has a speed of 362 m/s and a period of 4.17 ms,its wavelength is closest to:

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

Question 5

A crane lifts a 2500 kg mass 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)225 m/s
B)578 m/s
C)1220 m/s
D)1880 m/s
E)194 m/s

Question 6

Crests of an ocean wave pass a pier every 12.0 s.If the waves are moving at 5.6 m/s,what is the wavelength of the ocean waves?

A)67 m
B)34 m
C)77 m
D)57 m

Question 7

A motor drives a mechanism that produces simple harmonic motion at one end of a stretched cable such that the oscillation amplitude is 25.1 cm.What is the wave amplitude when the power of the motor is increased by 25.1%? Assume that the frequency oscillation and tension in the wire are unchanged.

A)28.1 cm
B)25.3 cm
C)30.9 cm
D)33.7 cm

Question 8

Transverse waves propagate at 43.2 m/s in a string that is subjected to a tension of 60.5 N.If the string is 15.9 m long,what is its mass?

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

Question 9

A 2.31 kg rope is stretched between supports 10.4 m apart.If one end of the rope is tweaked,how long will it take for the resulting disturbance to reach the other end? Assume that the tension in the rope is 74.4 N.

A)0.568 s
B)0.585 s
C)0.540 s
D)0.500 s

Question 10

A wire,1.0 m long,with a mass of 90 g,is under tension.A transverse wave is propagated on the wire,for which the frequency is 890 Hz,the wavelength is 0.10 m,and the amplitude is 6.5 mm.The tension in the line,in SI units,is closest to:

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

Question 11

A wave travels on a string with amplitude velocity v = 90.0 cm/s.If the tension on the string is increased by 20.0%,how much would the transmitted power on the string change if the wavelength is kept constant?

A)854%
B)90.0%
C)45%
D)The wavelength is needed.

Question 12

The velocity of a longitudinal sound wave in an ideal gas is given by v = ,where γ is the ratio of the specific heat at constant pressure to that at constant volume,P is the pressure,and ρ is the mass density.Assuming an ideal gas with γ = 1.4 and ρ = 1.4 g/l at standard temperature and pressure,find the wavelength for a 2700 Hz sound wave.

A)0.12 m
B)0.00 m
C)8.33 m
D)0.02 m

Question 13

The speed of sound in steel is 5000 m/s.What is the wavelength of a sound wave of frequency 660 Hz in steel?

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

Question 14

If a wave has a wavelength of 25.4 cm and a frequency of 1.63 kHz,its speed is closest to:

A)0.414 m/s
B)41.4 m/s
C)414 m/s
D)41,400 m/s
E)15.6 m/s

Question 15

A 4.24 m long,1.27 kg rope under a tension of 475 N oscillates with a frequency of 11.2 Hz.If the oscillation amplitude is 6.32 cm,how much energy is required to keep the rope oscillating for 5.52 s?

A)651 J
B)553 J
C)605 J
D)697 J

Question 16

The density of aluminum is 2700 kg/m³.If transverse waves propagate at 34 m/s in a 4.6 mm diameter aluminum wire,what is the tension on the wire?

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

Question 17

Radar involves using an electromagnetic wave to detect an object by observing the reflected energy from that object.Assume an aircraft has a radar cross section of 710 m²,and the receiving antenna has a cross section twice as large.If the aircraft is 50 km away,what percentage of the radiated energy is eventually detected?

A)1.0 × 10^-15
B)20
C)1.6 × 10^-13
D)0.00040

Question 18

A wave on a string,mass per unit length of 0.2 g/cm,travels in the z direction with the string displaced in the x and y directions as described by the equations
x = 5sin(kx - ωt)cm,and
Y = 5cos(kx - ωt)cm.
The wavelength and the wave velocity are γ = 11 cm and v = 6 cm/s respectively.What average power is transmitted along the string?

A)3.5 × 10^-5 W
B)3868 W
C)8.9 × 10^-7 W
D)5.9 × 10^-6 W

Question 19

A wire,6.0 m long,with a mass of 10 g,is under tension.A transverse wave is propagated on the wire,for which the frequency is 280 Hz,the wavelength is 0.60 m,and the amplitude is 8.4 mm.The time,for a crest of the transverse wave to travel the length of the wire,in ms,is closest to:

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

Question 20

Find the speed of an ocean wave whose displacement is given by y = 3.7 cos(2.2x - 5.6t)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 21

A wave pulse moves along a uniform string.The speed of this wave is constant but the speed of the particles of the string changes with time.

Question 22

You are generating traveling waves on a stretched string by wiggling one end.If you suddenly begin to wiggle more rapidly,you will cause the waves to travel faster down the string.

Question 23

Observer A is 2.0 m from a tiny light bulb and observer B is 8.0 m from the same bulb.The intensity of light from this bulb that A sees is 16 times as great as the intensity that B sees.

Question 24

If a rocket is traveling toward a mountain at 1/2 the speed of sound,the sound waves from this rocket's engine approach the mountain at 1 1/2 times the speed of sound.

Question 25

The howler monkey is the loudest land animal and can be heard up to a distance of 9.8 km.Assume the acoustic output of a howler to be uniform in all directions.The distance at which the intensity level of a howler's call is 25 dB,in SI units,is closest to:

A)550
B)660
C)830
D)940
E)1100

Question 26

The intensity of sunlight impinging on Earth is about 1.4 kW/m².What is the power emitted by the Sun in the spectrum of frequencies? (Earth-Sun distance = 1.5 × 10⁸ km,Earth 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 27

The sound from a truck moving at 17.00 m/s reflects from a cliff and is heard by an observer on the truck.What is the change in frequency for a wave with initial wavelength γ = 0.1500 m?

A)245 Hz
B)2281 Hz
C)2066 Hz
D)2400 Hz

Question 28

The siren of an ambulance wails at 1395 Hz when the ambulance is stationary.What frequency will you hear after this ambulance passes you while traveling at 33.60 m/s? The speed of sound under the prevailing conditions is 343.0 m/s.

A)1271 Hz
B)1547 Hz
C)1325 Hz
D)1465 Hz

Question 29

Situation 15.1
A train is approaching a signal tower at a speed of 40 m/s.The train engineer sounds the 1000 Hz whistle and a switchman in the tower responds by sounding the 1200 Hz siren.The air is still and the speed of sound is 340 m/s.
In Situation 15.1,the frequency of the train whistle tone,heard by the switchman,in SI units,is given by:

A)1000
B)300/340 × 1000
C)340/300 × 1000
D)340/380 × 1000
E)380/340 × 1000

Question 30

If you simultaneously send pulses of high frequency X rays and low frequency radio waves from Earth to the Moon,both waves will arrive at exactly the same time (assuming a vacuum between Earth and Moon).

Question 31

As light passes from air into glass,its wavelength decreases and its frequency increases so that its speed does not change.

Question 32

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 33

A weight W is hanging from a light vertical string.If a second weight W is added without stretching the string,the speed of pulses on this string will now be twice as great as it originally was.

Question 34

For a sound wave in air of frequency 3500 Hz and average intensity 1 W/m² (pain threshold)what is the maximum change in pressure (pressure amplitude)of the wave?

A)28.6 N/m²
B)816 N/m²
C)20.2 N/m²
D)3.18 × 10^-6 N/m²

Question 35

The howler monkey is the loudest land animal and can be heard up to a distance of 2.5 km.Assume the acoustic output of a howler to be uniform in all directions.The acoustic power emitted by the howler,in mW,is closest to:

A)0.079
B)0.026
C)0.26
D)0.79
E)2.6

Question 36

A glass window is installed in the window space and the intensity level of the sound entering through the window is reduced from 72 dB to 47 dB.The factor,by which the acoustic power entering the chamber is reduced by the glass window,is closest to:

A)3.2 × 10^-3
B)2.2 × 10^-2
C)5.6 × 10^-2
D)1.0 × 10^-1
E)1.5 × 10^-1

Question 37

What is the intensity level in decibels of a sound whose intensity is 10^-7 W/m²?

A)20 dB
B)30 dB
C)40 dB
D)50 dB
E)60 dB

Question 38

Situation 15.1
A train is approaching a signal tower at a speed of 40 m/s.The train engineer sounds the 1000 Hz whistle and a switchman in the tower responds by sounding the 1200 Hz siren.The air is still and the speed of sound is 340 m/s.
In Situation 15.1,the frequency of the tower siren tone,heard by the engineer,in SI units,is closest to:

A)1200
B)300/340 × 1200
C)340/300 × 1200
D)340/380 × 1200
E)380/340 × 1200

Question 39

Light from a laser forms a 1.31 mm diameter spot on a wall.If the light intensity in the spot is 3.69 x 10⁴ W/m²,what is the power output of the laser?

A)49.7 mW
B)30.8 mW
C)41.7 mW
D)57.7 mW

Question 40

Find the wavelength of a train whistle heard by a fixed observer as the train moves toward the observer with a velocity of 50.0 m/s.A wind blows at 5.0 m/s from the observer to the train.The whistle has a natural frequency of 500.0 Hz.

A)0.55 m
B)0.77 m
C)0.75 m
D)0.57 m

Question 41

Which of the following increases when a sound becomes louder?

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

Question 42

Suppose a water wave is moving radially outward on the surface of the water from a point source.How should the power in a small segment of the wave front depend on the radial distance from the source?

A)decrease as 1/r
B)decrease as 1/r2
C)independent of r
D)Not enough information

Question 43

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 44

Which of the following is a FALSE statement?

A)In a transverse wave the particle motion is perpendicular to the velocity vector of the wave.
B)Not all waves are mechanical in nature.
C)The speed of a wave and the speed of the vibrating particles that constitute the wave are different entities.
D)Waves transport energy and matter from one region to another.
E)A wave in which particles move back and forth in the same direction as the wave is moving is called a longitudinal wave.

Question 45

Which of the following forms is not a solution of the wave equation?

A)y = A sin(kx² - ωt²)
B)y = A sin(kx)cos(ωt)
C)y = A ∙ log(1/[kx - ωt]²)
D)y = A sin^-1([kx - ωt]³)