Deck 17: Wave Motion

Question 1

Which of the following is a solution to the wave equation, $\frac{\partial^{2} y}{\partial x^{2}}=\frac{1}{v^{2}} \frac{\partial^{2} y}{\partial t^{2}}$ ?

A) $\frac{e^{-x}}{x} \sin x$
B)(cos kx) (sin $\omega$ t)
C)e-x sin $\omega$ t
D)e-x sin (kx - $\omega$ t)
E)e-x cos t

Answer 1

(cos kx) (sin $\omega$ t)

Question 2

The wave equation is written down in an exam as: $\frac{d^{2} y}{d x^{2}}=v^{2} \frac{d^{2} y}{d t^{2}}$ From dimensional considerations we see that:

A)v2 should be replaced by $\frac{T}{\mu}$ .
B)v2 should be replaced by $\sqrt{\frac{T}{\mu}}$ .
C)v2 should be replaced by v.
D)v2 should be replaced by $\frac{1}{v}$ .
E)v2 should be replaced by $\frac{1}{v^{2}}$ .

Answer 2

v2 should be replaced by $\frac{1}{v^{2}}$ .

Question 3

Bats can detect small objects such as insects that are of a size in the order of a wavelength. If bats emit a chirp at a frequency of 60 kHz and the speed of sound waves in air is 330 m/s, what is the smallest size insect they can detect?

A)1.5 mm
B)3.5 mm
C)5.5 mm
D)7.5 mm
E)9.8 mm

Answer 3

5.5 mm

Question 4

For the transverse wave described by $y=0.15 \sin \left[\frac{\pi}{16}(2 x-64 t)\right] \text { (SI units) }$ , determine the maximum transverse speed of the particles of the medium.

A)0.192 m/s
B)0.6 $\pi$ m/s
C)9.6 m/s
D)4 m/s
E)2 m/s

Question 5

If y = 0.02 sin (30x - 400t) (SI units), the velocity of the wave is:

A)3/40 m/s.
B)40/3 m/s.
C)60 $\pi$ /400 m/s.
D)400/60 $\pi$ m/s.
E)400 m/s.

Question 6

A pulse is described by $y=3 /\left[(x+2 t)^{2}+4\right]$ in SI units. What is the velocity of the pulse?

A)3 m/s in the +x direction
B)2 m/s in the -x direction
C)2 m/s in the +x direction
D)4 m/s in the -x direction
E)4 m/s in the +x direction

Question 7

The wavelength of light visible to the human eye is in the order of 5 *10-7 m. If the speed of light in air is 3 *108 m/s, find the frequency of the lightwave.

A)3 * 107 Hz
B)4 * 109 Hz
C)5 * 1011 Hz
D)6 *1014 Hz
E)4 *1015 Hz

Question 8

For the wave described by $y=0.15 \sin \left[\frac{\pi}{16}(2 x-64 t)\right] \text { (SI units) }$ , determine the first positive x coordinate where y is a maximum when t = 0.

A)16 m
B)8 m
C)4 m
D)2 m
E)13 m

Question 9

You are holding on to one end of a long string that is fastened to a rigid steel light pole. After producing a wave pulse that was 5 mm high and 4 cm wide, you want to produce a pulse that is 4 cm wide but 7 mm high. You must move your hand up and down once:

A)the same distance up as before, but take a shorter time.
B)the same distance up as before, but take a longer time.
C)a smaller distance up, but take a shorter time.
D)a greater distance up, but take a longer time.
E)a greater distance up, but take the same time.

Question 10

The lowest A on a piano has a frequency of 27.5 Hz. If the tension in the 2.00-m string is 308 N, and one-half wavelength occupies the string, what is the mass of the wire?

A)0.025 kg
B)0.049 kg
C)0.051 kg
D)0.081 kg
E)0.037 kg

Question 11

Refer to Exhibit 17-1 below.Exhibit 17-1 The figure below shows a sine wave on a string at one instant of time. Which of the graphs below shows a wave where the wavelength is twice as large?

A)
B)
C)
D)
E)

Question 12

If y = 0.02 sin (30x - 400t) (SI units), the frequency of the wave is:

A)30 Hz
B)15/ $\pi$ Hz
C)200/ $\pi$ Hz
D)400 Hz
E)800 $\pi$ Hz

Question 13

Refer to Exhibit 17-1 below.Exhibit 17-1 The figure below shows a sine wave on a string at one instant of time. Which of the graphs below shows a wave where the frequency and wave velocity are both doubled?

A)
B)
C)
D)
E)

Question 14

Ocean waves with a wavelength of 120 m are coming in at a rate of 8 per minute. What is their speed?

A)8.0 m/s
B)16 m/s
C)24 m/s
D)30 m/s
E)4.0 m/s

Question 15

The figure below represents a string, which has a heavy section and a light section. The mass per unit length of the heavy section is 16 times as large as the mass per unit length of the light section. When the string is under tension, the speed of a pulse travelling in the heavy section is ____ times the speed of that same pulse travelling in the light section.

A) $\frac{1}{16}$
B) $\frac{1}{4}$
C) $\frac{1}{2}$
D)2
E)4

Question 16

An earthquake emits both S-waves and P-waves, which travel at different speeds through the Earth. A P-wave travels at 9000 m/s and an S-wave travels at 5000 m/s. If P-waves are received at a seismic station 1.00 minute before an S-wave arrives, how far away is the earthquake centre?

A)88.9 km
B)1200 km
C)675 km
D)240 km
E)480 km

Question 17

Find the period of a wave of 100-m wavelength in deep water where $v=\sqrt{g \lambda / 2 \pi}$ .

A)5.0 s
B)8.0 s
C)12.5 s
D)15 s
E)0.125 s

Question 18

Write the equation of a wave, travelling along the +x axis with an amplitude of 0.02 m, a frequency of 440 Hz, and a speed of 330 m/sec.

A)y = 0.02 sin [880 $\pi$ (x/330 -t)]
B)y = 0.02 cos [880 $\pi$ x/330 -440t]
C)y = 0.02 sin [880 $\pi$ (x/330 + t)]
D)y = 0.02 sin [2 $\pi$ (x/330 + 440t)]
E)y = 0.02 cos [2 $\pi$ 0(x/330 + 440t)]

Question 19

A piano wire of length 1.5 m vibrates so that one-half wavelength is contained on the string. If the frequency of vibration is 65 Hz, the amplitude of vibration is 3.0 mm, and the density is 15 g/m, how much energy is transmitted per second down the wire?

A)21 W
B)11 W
C)5.4 W
D)2.2 W
E)1.1 W

Question 20

A piano string of density 0.005 0 kg/m is under a tension of 1350 N. Find the velocity with which a wave travels on the string.

A)260 m/s
B)520 m/s
C)1040 m/s
D)2080 m/s
E)4160 m/s

Question 21

A stone is thrown into a quiet pool of water. With no fluid friction, the amplitude of the waves falls off with distance r from the impact point as:

A)1/r3
B)1/r2
C)1/r3/2
D)1/r1/2
E)1/r

Question 22

Calculate the pressure amplitude (in N/m²) of a 500 Hz sound wave in helium if the displacement amplitude is equal to 5.0 *10-8 m. ( $\rho$ = 0.179 kg/m3, v = 972 m/s.)

A)3.5* 10-2
B)1.6 *10-2
C)2.7 * 10-2
D)4.2 * 10-2
E)2.0 *10-2

Question 23

The variation in the pressure of helium gas, measured from its equilibrium value, is given by $\Delta$ P = 2.9 * 10-5 cos (6.20x - 3 000t) where x and t have units m and s, and $\Delta$ P is measured in N/m². Determine the frequency (in Hz) of the wave.

A)1500
B)477
C)1.01
D)0.32
E)239

Question 24

A jet plane has a sound level of 150 dB. What is the intensity in W/m²?

A)1
B)100
C)10
D)1000
E)10°000

Question 25

A boy has climbed to the top of a 6.00 m tall tree. When he shouts, the sound waves have an intensity of $0.250 \frac{\mathrm{~W}}{\mathrm{~m}^{2}}$ at a 1.00 m distance from the top of the tree. The ratio of intensity at the base of the tree to the intensity 1.00 m from the top of the tree is:

A) $\frac{1}{36}$ .
B) $\frac{1}{25}$ .
C) $\frac{1}{6}$ .
D) $\frac{1}{5}$ .
E) $\frac{1}{\sqrt{6}}$ .

Question 26

The velocity of sound in sea water is 1.53 * 103 m/s. Find the bulk modulus (in N/m²) of sea water if its density is 1.03 *103 kg/m3.

A)2.57 * 109
B)2.19 * 109
C)2.04 * 109
D)2.41 * 109
E)2.82 * 109

Question 27

When you hear the horn of a car that is approaching you, the frequency that you hear is larger than that heard by a person in the car because for the sound you hear:

A)wave crests are farther apart by the distance the car travels in one period.
B)wave crests are closer together by the distance the car travels in one period.
C)the car gets ahead of each wave crest before it emits the next one.
D)the speed of sound in air is increased by the speed of the car.
E)a speeding car emits more wavecrests in each period.

Question 28

A source of sound waves is placed at the centre of a very large sound-reflecting wall. The source emits 0.500 W of power. Two metres from the source the intensity in W/m² is:

A)9.95*10-3.
B)1.99 * 10-2.
C)0.313.
D)0.399.
E)0.625.

Question 29

Determine the intensity (in W/m²) of a harmonic longitudinal wave with a pressure amplitude of 8.0 * 10-3 N/m² propagating down a tube filled with helium. ( $\rho$ = 0.179 kg/m3, v = 972 m/s.)

A)3.7 * 10-7
B)1.8 *10-7
C)9.2 *10-8
D)4.6*10-8
E)1.5* 10-9

Question 30

What is the expression for the transverse velocity of the wave in a string given by ?

A)
B)
C)
D)
E)

Question 31

By what factor is the intensity of sound at a rock concert louder than that of a whisper when the two intensity levels are 120 dB and 20 dB respectively?

A)1012
B)108
C)106
D)1010
E)1011

Question 32

A wave generated in a medium is a longitudinal wave when:

A)there is a net transport of matter by the wave.
B)the molecules of the medium are unable to exert forces on each other.
C)molecular displacements are parallel to the wave velocity.
D)molecular displacements are perpendicular to the wave velocity.
E)the density of the medium is less than the density of water.

Question 33

A car approaches a stationary police car at 36 m/s. The frequency of the siren (relative to the police car) is 500 Hz. What is the frequency (in Hz) heard by an observer in the moving car as he approaches the police car? (Assume the velocity of sound in air is 343 m/s.)

A)220
B)448
C)526
D)552
E)383

Question 34

A truck moving at 36 m/s passes a police car moving at 45 m/s in the opposite direction. If the frequency of the siren is 500 Hz relative to the police car, what is the change in frequency (in Hz) heard by an observer in the truck as the two vehicles pass each other? (The speed of sound in air is 343 m/s.)

A)242
B)238
C)240
D)236
E)234

Question 35

To decrease the intensity of the sound you are hearing from your speaker system by a factor of 36, you can

A)reduce the amplitude by a factor of 12 and increase your distance from the speaker by a factor of 3.
B)reduce the amplitude by a factor of 4 and increase your distance from the speaker by a factor of 3.
C)reduce the amplitude by a factor of 2 and increase your distance from the speaker by a factor of 3.
D)reduce the amplitude by a factor of 3 and increase your distance from the speaker by a factor of 4.
E)reduce the amplitude by a factor of 3 and increase your distance from the speaker by a factor of 12.

Question 36

It is possible to hear an approaching train before you can see it by listening to the sound wave through the track. If the elastic modulus is 2.0*1011 N/m² and the density of steel is 7.8 *103 kg/m3, approximately how many times faster is the speed of sound in the track than in air? (vair $\approx$ 340 m/s.)

A)20
B)5
C)10
D)15
E)25

Question 37

A point source emits sound with a power output of 100 watts. What is the intensity (in W/m²) at a distance of 10.0 m from the source?

A)7.96 * 10-2
B)7.96 *10-1
C)7.96 *100
D)7.96 *01
E)7.96 *10-3

Question 38

A boat sounds a fog horn on a day when both the sea water and the air temperature are 25.0 $\degree$ C. The speed of sound in sea water is 1533 m/s. How much earlier (in s) does a dolphin 1000 m from the source hear the sound than a person in a boat that is also 1000 m distant? (Ignore the time it takes the sound to reach the water surface.)

A)0.652
B)2.12
C)2.24
D)2.77
E)2.90

Question 39

The Young's modulus for aluminum is 7.02 *1010 N/m². If the speed of sound in aluminum is measured to be 5.10 km/s, find its density (in kg/m3).

A)11.3 * 103
B)7.80 * 103
C)2.70 *103
D)29.3 * 103
E)1.40 *103

Question 40

The fundamental frequency of A above middle C on the piano is 440 Hz. This is the tenor high A, but a convenient note in the mid-range of women's voices. When we calculate the wavelength, we find that it is:

A)much shorter than the length of either a man's or woman's lips.
B)shorter than the length of a man's lips, but about the length of a woman's lips.
C)longer than a woman's lips, but about the length of a man's lips.
D)much longer than the length of either a man's or a woman's lips.
E)about the same length as either a man's or woman's lips.

Question 41

A bat, flying at 5.00 m/s, emits a chirp at 40.0 kHz. If this sound pulse is reflected by a wall, what is the frequency of the echo received by the bat? (vsound = 340 m/s.)

Question 42

A circus performer stretches a tightrope between two towers. He strikes one end of the rope and sends a wave along it toward the other tower. He notes that it takes 0.8 s for the wave to travel the 20 m to the opposite tower. If one metre of the rope has a mass of 0.35 kg, find the tension in the tightrope.

Question 43

Bats can detect small objects such as insects that are of a size approximately that of one wavelength. If bats emit a chirp at a frequency of 60 kHz, and the speed of sound in air is 340 m/s, what is the smallest size insect they can detect?

Question 44

When a workman strikes a steel pipeline with a hammer, he generates both longitudinal and transverse waves. The two types of reflected waves return 2.4 s apart. How far away is the reflection point? (For steel, vL = 6.2 km/s, vT = 3.2 km/s)

Question 45

If a plane is flying at a speed so that the apex half-angle of its shockwave is 30 $\degree$ , what is its speed if the speed of sound is 320 m/s?

A)960 m/s
B)640 m/s
C)320 m/s
D)160 m/s
E)Choose this answer if a shock wave cannot form in this situation.

Question 46

The intensity level of an orchestra is 85 dB. A single violin achieves a level of 70 dB. How does the intensity of the sound of the full orchestra compare with that of the violin?

Question 47

A microphone in the ocean is sensitive to the sounds emitted by dolphins. To produce a usable signal, sound waves striking the microphone must have an intensity of 1.02 *10-11 W/m². If dolphins emit sounds with a power of 0.049 9 W, how far away can a dolphin be and still be heard? Disregard absorption of sound waves by the water.

Question 48

An aircraft travelling at half the speed of sound emits sound at a frequency of 5000 Hz. At what frequency does a stationary listener hear the sound as the plane approaches, and after it passes by? Assume the aircraft is not flying very high.

Question 49

If the breakers at a beach are separated by 5.0 m and hit shore with a frequency of 0.20 Hz, with what speed are they travelling?

Question 50

If a supersonic plane is flying at increasing speed as the temperature decreases, what happens to the Mach number in this instance?

A)It stays the same.
B)It increases.
C)It decreases.
D)It can do any of the above.
E)It can do either (a) or (b) but not (c).