Deck 17: Traveling Waves

Question 1

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.

Answer 1

π/15 m.

Question 2

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

Answer 2

4 m

Question 3

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

Answer 3

20 m

Question 4

A piano string of density 0.0050 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 5

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 6

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)1500 m/s

Question 7

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 8

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 9

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 10

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 11

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 12

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 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 center?

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

Question 13

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 14

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 15

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 16

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 17

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 18

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)1000 Hz
D)2000 Hz
E)2500 Hz

Question 19

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 20

The speed of a 10-kHz sound wave in seawater is approximately 1500 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 21

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 22

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).
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 23

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 24

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 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

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).
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

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 28

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 29

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 30

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

A)
B)
C)
D)
E)

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

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

A)
B)
C)
D)
E)

Question 33

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 34

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 35

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).
Which of the graphs below shows a wave where the amplitude and the frequency are doubled?

A)
B)
C)
D)
E)

Question 36

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 37

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).
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 38

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 39

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 40

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).
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 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

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 45

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

A)
B)
C)
D)
E)

Question 46

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?