Deck 16: Wave Motion

Question 1

The wavelength of light visible to the human eye is on 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

Answer 1

6 × 10¹⁴ Hz

Question 2

For the transverse wave described by , determine the maximum transverse speed of the particles of the medium.

A) 0.192 m/s
B) 0.6π m/s
C) 9.6 m/s
D) 4 m/s
E) 2 m/s

Answer 2

0.6π m/s

Question 3

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

A) 30 rad/s
B) 30/2π rad/s
C) 400/2π rad/s
D) 400 rad/s
E) 40/3 rad/s

Answer 3

400 rad/s

Question 4

For the wave described by , determine the x coordinate of the second maximum when t = 0.

A) 20 m
B) 18 m
C) 24 m
D) 28 m
E) 16 m

Question 5

Write the equation of a wave, traveling 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 [880π(x/330 − t)]
B) y = 0.02 cos [880π x/330 − 440t]
C) y = 0.02 sin [880π(x/330 + t)]
D) y = 0.02 sin [2π(x/330 + 440t)]
E) y = 0.02 cos [2π(x/330 + 440t)]

Question 6

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

A) 30 Hz
B) 15/π Hz
C) 200/π Hz
D) 400 Hz
E) 800π Hz

Question 7

If y = 0.02 sin (30x − 400t) (SI units), the wavelength of the wave is

A) π/15 m
B) 15/π m
C) 60π m
D) 4.2 m
E) 30 m

Question 8

A 100-m long transmission cable is suspended between two towers. If the mass density is 2.01 kg/m and the tension in the cable is 3.00 × 10⁴ N, what is the speed of transverse waves on the cable?

A) 60 m/s
B) 122 m/s
C) 244 m/s
D) 310 m/s
E) 1 500 m/s

Question 9

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 10

Bats can detect small objects such as insects that are of a size on the order of a wavelength. If bats emit a chirp at a frequency of 60 kHz and the speed of soundwaves 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

Question 11

Transverse waves are traveling on a 1.00-m long piano string at 500 m/s. If the points of zero vibration occur at one-half wavelength (where the string is fastened at both ends), find the frequency of vibration.

A) 250 Hz
B) 500 Hz
C) 1 000 Hz
D) 2 000 Hz
E) 2 500 Hz

Question 12

If y = 0.02 sin (30x − 400t) (SI units) and if the mass density of the string on which the wave propagates is 0.005 kg/m, then the transmitted power is

A) 1.03 W
B) 2.13 W
C) 4.84 W
D) 5.54 W
E) 106 W

Question 13

An earthquake emits both S-waves and P-waves which travel at different speeds through the Earth. A P-wave travels at 9 000 m/s and an S-wave travels at 5 000 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 center?

A) 88.9 km
B) 1 200 km
C) 675 km
D) 240 km
E) 480 km

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

A piano string of density 0.005 0 kg/m is under a tension of 1 350 N. Find the velocity with which a wave travels on the string.

A) 260 m/s
B) 520 m/s
C) 1 040 m/s
D) 2 080 m/s
E) 4 160 m/s

Question 16

The speed of a 10-kHz sound wave in seawater is approximately 1 500 m/s. What is its wavelength in sea water?

A) 5.0 cm
B) 10 cm
C) 15 cm
D) 20 cm
E) 29 cm

Question 17

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) 60π/400 m/s
D) 400/60π m/s
E) 400 m/s

Question 18

For the wave described by , 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 19

For the wave described by y = 0.02 sin (kx) at t = 0 s, the first maximum at a positive x coordinate occurs where x = 4 m. Where on the positive x axis does the second maximum occur?

A) 20 m
B) 18 m
C) 24 m
D) 28 m
E) 16 m

Question 20

If y = 0.02 sin (30x − 400t) (SI units), the wave number is

A) 30 rad/m
B) 30/2π rad/m
C) 400/2π rad/m
D) 400 rad/m
E) 60π rad/m

Question 21

To transmit four times as much energy per unit time along a string, you can

A) double the frequency.
B) double the amplitude.
C) increase the tension by a factor of 16.
D) do any one of the above.
E) do only (a) or (b) above.

Question 22

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 6 cm wide and 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 23

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 traveling in the heavy section is ____ times the speed of that same pulse traveling in the light section.

A)

B)

C)

D) 2
E) 4

Question 24

Exhibit 16-3
Four wave functions are given below.
I.y(x, t) = 5sin(4x - 20t + 4)
II.y(x, t) = 5sin(3x - 12t + 5)
III.y(x, t) = 5cos(4x + 24t + 6)
IV.y(x, t) = 14cos(2x - 8t + 3)
Use this exhibit to answer the following question(s).
Refer to Exhibit 16-3. Rank the wave functions in order of the magnitude of the wave speeds, from least to greatest.

A) IV, II, I, III
B) IV = II, I, III
C) III, I, II, IV
D) IV, I, II, III
E) III, IV, II, I

Question 25

A student attaches a length of nylon fishing line to a fence post. She stretches it out and shakes the end of the rope in her hand back and forth to produce waves on the line. The most efficient way for her to increase the wavelength is to

A) increase the tension on the hose and shake the end more times per second.
B) decrease the tension on the hose and shake the end more times per second.
C) increase the tension on the hose and shake the end fewer times per second.
D) decrease the tension on the hose and shake the end fewer times per second.
E) keep the tension and frequency the same but increase the length of the hose.

Question 26

Exhibit 16-1
The figure below shows a sine wave at one point of a string as a function of time. Use the exhibit to answer the following question(s).
Refer to Exhibit 16-1. Which of the graphs below shows a wave where the amplitude and frequency are each reduced in half?

A)

B)

C)

D)

E)

Question 27

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 28

Exhibit 16-3
Four wave functions are given below.
I.y(x, t) = 5sin(4x - 20t + 4)
II.y(x, t) = 5sin(3x - 12t + 5)
III.y(x, t) = 5cos(4x + 24t + 6)
IV.y(x, t) = 14cos(2x - 8t + 3)
Use this exhibit to answer the following question(s).
Refer to Exhibit 16-3. Rank the wave functions in order of the magnitude of the wavelengths, from least to greatest.

A) IV, II, I, III
B) IV, I, II, III
C) I, II, III, IV
D) IV, II, III = I
E) I = III, II, IV

Question 29

Suppose that you were selected for a "Survivor"-type TV show. To help keep your group connected, you suggest that long vines can be tied together and used to transmit signals in cases of emergency. To get the signals to travel faster, you should

A) select lighter vines.
B) increase the tension on the vines.
C) hang weights from the vines at evenly spaced intervals.
D) do all of the above.
E) do (a) or (b) above, preferably both.

Question 30

The wave equation is written down in an exam as From dimensional considerations we see that

A) v² should be replaced by
.
B) v² should be replaced by
.
C) v² should be replaced by v.
D) v² should be replaced by
.
E) v² should be replaced by
.

Question 31

Find the period of a wave of 100-m wavelength in deep water where .

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

Question 32

Ariel claims that a pulse is described by the equation where x and y are measured in cm and t in s. Miranda says that it is not possible to represent a pulse with this function because a wave must be a function of x + vt or x − vt. Which one, if either, is correct, and why?

A) Ariel, because x² - 6.0xt + 9t² = (x - 3.0t)².
B) Ariel, because a pulse is not an infinite wave.
C) Miranda, because (x - 3.0t)² is the same as (3.0t - x)².
D) Miranda, because a pulse is not an infinite wave.
E) Miranda, because
is infinite when x = 0.

Question 33

Exhibit 16-1
The figure below shows a sine wave at one point of a string as a function of time. Use the exhibit to answer the following question(s).
Refer to Exhibit 16-1. Which of the graphs below shows a wave where the amplitude and the frequency are doubled?

A)

B)

C)

D)

E)

Question 34

Earthquake waves are classified as P waves and S waves. Which of the following statements is true about these waves?

A) The P wave is transverse as is the S wave.
B) The P wave is longitudinal as is the S wave.
C) The P wave is transverse and the S wave is longitudinal.
D) The P wave is longitudinal and the S wave is transverse.
E) Both the P and S waves are mixtures of longitudinal and transverse waves.

Question 35

Exhibit 16-3
Four wave functions are given below.
I.y(x, t) = 5sin(4x - 20t + 4)
II.y(x, t) = 5sin(3x - 12t + 5)
III.y(x, t) = 5cos(4x + 24t + 6)
IV.y(x, t) = 14cos(2x - 8t + 3)
Use this exhibit to answer the following question(s).
Refer to Exhibit 16-3. Rank the wave functions in order of the magnitude of the frequencies of the waves, from least to greatest.

A) IV, II, I, III
B) IV = II, I, III
C) III, I, II, IV
D) IV, I, II, III
E) III, IV, II, I

Question 36

Which of the following is a solution to the wave equation, ?

A)

B) (cos kx) (sin ωt)
C) e−x sin ωt
D) e−x sin (kx − ωt)
E) e−x cos t

Question 37

Exhibit 16-2
The figure below shows a sine wave on a string at one instant of time. Use this exhibit to answer the following question(s).
Refer to Exhibit 16-2. Which of the graphs below shows a wave where the wavelength is twice as large?

A)

B)

C)

D)

E)

Question 38

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 39

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 6 cm wide but still 5 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 40

Exhibit 16-2
The figure below shows a sine wave on a string at one instant of time. Use this exhibit to answer the following question(s).
Refer to Exhibit 16-2. Which of the graphs below shows a wave where the frequency and wave velocity are both doubled?

A)

B)

C)

D)

E)

Question 41

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 traveling?

Question 42

A pulse is described by 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 43

The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10−⁵ cos (6.20x − 3 000t) where x and t have units m and s, and ΔP is measured in N/m². Determine the wavelength (in m) of the wave.

A) 1 500
B) 0.32
C) 477
D) 1.01
E) 0.50

Question 44

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

A) 1 500
B) 477
C) 1.01
D) 0.32
E) 239

Question 45

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 46

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 47

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? (v_air ≈ 340 m/s.)

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

Question 48

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. (ρ = 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 49

A sculptor strikes a piece of marble with a hammer. Find the speed of sound through the marble (in km/s). (The Young's modulus is 50 × 10⁹ N/m² and its density is 2.7 × 10³ kg/m³.)

A) 5.1
B) 4.3
C) 3.5
D) 1.3
E) 1.8

Question 50

By what factor will an intensity change when the corresponding sound level increases by 3 dB?

A) 3
B) 0.5
C) 2
D) 4
E) 0.3

Question 51

The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10−⁵ cos (6.20x − 3 000t) where x and t have units m and s. Determine the speed (in m/s) of the wave.

A) 1 515
B) 153
C) 484
D) 828
E) 101

Question 52

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 53

Calculate the intensity level in dB of a sound wave that has an intensity of 15 × 10−⁴ W/m².

A) 20
B) 200
C) 92
D) 9
E) 10

Question 54

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 55

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. (ρ = 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 56

Calculate the displacement amplitude (in m) of a 20 kHz sound wave in helium if it has a pressure amplitude of 8.0 × 10−³ N/m². (ρ = 0.179 kg/m³, v = 972 m/s.)

A) 2.9 × 10−¹⁰
B) 3.7 × 10−¹⁰
C) 7.8 × 10−⁹
D) 2.4 × 10−⁹
E) 1.9 × 10−¹⁰

Question 57

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

A) 1
B) 100
C) 10
D) 1 000
E) 10 000

Question 58

The equation is the same as

A)

B)

C)

D)

E)

Question 59

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

A)

B)

C)

D)

E)

Question 60

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 meter of the rope has a mass of 0.35 kg, find the tension in the tightrope.

Question 61

A point source emits sound waves with a power output of 100 watts. What is the sound level (in dB) at a distance of 10 m?

A) 139
B) 119
C) 129
D) 109
E) 10

Question 62

A spherical wave has the form . The wavelength of the wave is

A) 0.25 m.
B) 0.50 m.
C) 4.0 m.
D) 8.0 m.
E) 4.0π m.

Question 63

A boy has climbed to the top of a 6.00 m tall tree. When he shouts, the sound waves have an intensity of 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)
.
B)
.
C)
.
D)
.
E)
.

Question 64

A spherical wave has the form . The velocity of the wave (in m/s) is

A) 0.005 88.
B) 16.0
C) 340.
D) 1 360.
E) 2 720.

Question 65

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 frequency heard by an observer in the truck after the police car passes the truck? (The speed of sound in air is 343 m/s.)

A) 361
B) 636
C) 393
D) 396
E) 383

Question 66

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 67

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 68

A person standing in the street is unaware of a bird dropping that is falling from a point directly above him with increasing velocity. If the dropping were producing sound of a fixed frequency, as it approaches the person would hear the sound

A) drop in frequency.
B) stay at the same frequency.
C) increase in frequency.
D) decrease in loudness.
E) stay at the same loudness.

Question 69

(Do not try the following: it could kill you. This question is only about a hypothetical possibility.) If you were standing below an object emitting a fixed frequency sound falling at terminal velocity, as it approached you, you would hear the sound

A) drop in frequency.
B) stay at the same frequency.
C) increase in frequency.
D) decrease in loudness.
E) stay at the same loudness.

Question 70

A spherical wave has the form . The amplitude of the wave a distance r from the source is

A) 0.002 cm.
B)
.
C)
.
D)
.
E)
.

Question 71

A spherical wave has the form . The frequency of the wave (in Hz) is

A) 3.68 × 10−⁴.
B) 7.35 × 10−⁴.
C) 1 360.
D) 2 720.
E) 2 720π.

Question 72

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 73

A car moving at 36 m/s passes a stationary police car whose siren has a frequency of 500 hz. What is the change in the frequency (in Hz) heard by an observer in the moving car as he passes the police car? (The speed of sound in air is 343 m/s.)

A) 416
B) 208
C) 105
D) 52
E) 552

Question 74

How fast (in m/s) is the Concorde moving if it reaches Mach 1.5? (The speed of sound in air is 344 m/s.)

A) 229
B) 516
C) 416
D) 728
E) 858

Question 75

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 76

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 relative to the police car is 500 Hz, what is the frequency heard by an observer in the truck as the police car approaches the truck? (The speed of sound in air is 343 m/s.)

A) 396
B) 636
C) 361
D) 393
E) 617

Question 77

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 × 10¹
E) 7.96 × 10−³

Question 78

While you are sounding a tone on a toy whistle, you notice a friend running toward you. If you want her to hear the same frequency that you hear even though she is approaching, you must

A) stay put.
B) run towards her at the same speed.
C) run away from her at the same speed.
D) stay put and play a note of higher frequency.
E) run towards her and play a note of higher frequency.

Question 79

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/r^3/2
D) 1/r^1/2
E) 1/r

Question 80

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.