Deck 16: Wave Motion

Question 1

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

Answer 1

200/π Hz

Question 2

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

Answer 2

16 m/s

Question 3

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)]

Answer 3

y = 0.02 sin [880π(x/330 − t)]

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

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 6

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 7

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 8

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 9

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 10

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 11

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

Question 12

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 13

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 14

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 15

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

Question 16

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 17

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

Question 18

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 19

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 20

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 21

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 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 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 23

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 24

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 25

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 26

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 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 16-1
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 29

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 30

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 31

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 32

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 33

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 34

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 35

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 36

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 37

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 38

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 39

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 40

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 41

The equation
Is the same as

A)
B)
C)
D)
E)

Question 42

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 43

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 44

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

A)
B)
C)
D)
E)

Question 45

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 46

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.