Deck 14: Mechanical Waves

Question 1

A tube open at one end and closed at the other end produces sound having a fundamental frequency of 350 Hz. If you now open the closed end, the fundamental frequency becomes

A) 87.5 Hz.
B) 175 Hz.
C) 350 Hz.
D) 700 Hz.
E) 1400 Hz.

Answer 1

175 Hz.

Question 2

When a weight W is hanging from a light vertical string, the speed of pulses on the string is V. If a second weight W is added without stretching the string, the speed of pulses on this string will now become

A) 2V.
B) V.
C) V.
D) V/ .
E) V/2

Answer 2

V.

Question 3

A transverse wave is traveling on a string stretched along the horizontal x-axis. The equation for the vertical displacement y of the string is given by y = 0.0020 cos[π(15x - 52t)], where all quantities are in SI units. The maximum speed of a particle of the string is closest to

A) 0.33 m/s.
B) 0.43 m/s.
C) 0.53 m/s.
D) 0.64 m/s.
E) 0.74 m/s.

Answer 3

0.33 m/s.

Question 4

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 5

You are generating traveling waves on a stretched string by wiggling one end. If you suddenly begin to wiggle more rapidly without appreciably affecting the tension, you will cause the waves to move down the string

A) faster than before.
B) slower than before.
C) at the same speed as before.

Question 6

The vertical displacement y(x,t) of a string stretched along the horizontal x-axis is given by y(x,t) = (6.00 mm) cos[(3.25 m-1)x - (7.22 rad/s)t].
(a) What is the minimum time for each complete cycle of the wave?
(b) What is the distance between adjacent crests of the wave?
(c) How fast does this wave travel?

Question 7

A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thicker and heavier. What is the orientation of the reflected and transmitted pulses?

A) Both pulses are right side up.
B) The reflected pulse returns right side up while the transmitted pulse is inverted.
C) The reflected pulse returns inverted while the transmitted pulse is right side up.
D) Both pulses are inverted.

Question 8

The figure shows the displacement y of a traveling wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. Determine the wavelength of the wave.

A) 2.0 cm
B) 3.0 m
C) 2.0 m
D) 4.0 m
E) 1.5 m

Question 9

The figure shows the displacement y of a wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. Determine the frequency of the wave.

A) 4.0 Hz
B) 0.50 Hz
C) 3.0 Hz
D) 0.33 Hz
E) 0.25 Hz

Question 10

A guitar string is fixed at both ends. If you tighten it to increase its tension

A) the frequencies of its vibrational modes will increase but its wavelengths will not be affected.
B) the wavelength increases but the frequency is not affected.
C) both the frequency and the wavelength increase.

Question 11

For the wave shown in the figure, the frequency is

A) 0.5 Hz.
B) 1 Hz.
C) 2 Hz.
D) 4 Hz.
E) unable to be determined from the given information.

Question 12

Four traveling waves are described by the following equations, where all quantities are measured in SI units and y represents the displacement.
I: y = 0.12 cos(3x - 21t)
II: y = 0.15 sin(6x + 42t)
III: y = 0.13 cos(6x + 21t)
IV: y = -0.27 sin(3x - 42t)
Which of these waves have the same period?

A) I and III, and also II and IV
B) I and IV, and also II and III
C) I and II, and also III and IV
D) All of them have the same period.
E) They all have different periods.

Question 13

Four traveling waves are described by the following equations, where all quantities are measured in SI units and y represents the displacement.
I: y = 0.12 cos(3x + 2t)
II: y = 0.15 sin(6x - 3t)
III: y = 0.23 cos(3x + 6t)
IV: y = -0.29 sin(1.5x - t)
Which of these waves have the same speed?

A) I and III
B) I and IV
C) II and III
D) I and II
E) III and IV

Question 14

Ocean tides are waves that have a period of 12 hours, an amplitude (in some places) of 1.50 m, and a speed of 750 km/hr. What is the distance between adjacent crests of these waves?

A) 9000 km
B) 32,400 km
C) 9000 m
D) 32,400 m
E) 2500 m

Question 15

The figure shows the displacement y of a traveling wave at a given position as a function of time and the displacement of the same wave at a given time as a function of position. How fast is the wave traveling?

A) 3.0 m/s
B) 0.75 m/s
C) 0.66 m/s
D) 1.5 m/s
E) 2.0 m/s

Question 16

Find the speed of an ocean wave whose vertical displacement y as a function of time t is given by y(x,t) = 3.7 cos(2.2x - 5.6t), where all quantities are in SI units.

A) 2.5 m/s
B) 1.9 m/s
C) 3.5 m/s
D) 4.5 m/s

Question 17

A wave pulse traveling to the right along a thin cord reaches a discontinuity where the rope becomes thinner and lighter. What is the orientation of the reflected and transmitted pulses?

A) Both pulses are right side up.
B) The reflected pulse returns right side up while the transmitted pulse is inverted.
C) The reflected pulse returns inverted while the transmitted pulse is right side up.
D) Both pulses are inverted.

Question 18

For the wave shown in the figure, the wavelength is

A) 8 m.
B) 4 m.
C) 2 m.
D) 1 m.
E) unable to be determined from the given information.

Question 19

A transverse wave traveling along a string transports energy at a rate r. If we want to double this rate, we could

A) increase the amplitude of the wave by a factor of 8.
B) increase the amplitude of the wave by a factor of 4.
C) increase the amplitude of the wave by a factor of 2.
D) increase the amplitude by a factor of .
E) increase the amplitude by a factor of .

Question 20

Consider the waves on a vibrating guitar string and the sound waves the guitar produces in the surrounding air. The string waves and the sound waves must have the same

A) wavelength.
B) velocity.
C) frequency.
D) amplitude.
E) More than one of the above is true.

Question 21

A 1.0-g string that is 0.64 m long is fixed at both ends and is under tension. This string produces a 100-Hz tone when it vibrates in the third harmonic. The speed of sound in air is 344 m/s. The tension in the string, in is closest to

A) 2.8 N.
B) 2.3 N.
C) 1.8 N.
D) 3.4 N.
E) 3.9 N.

Question 22

The intensity of sunlight falling on the earth is about 1.4 kW/m2 (before any gets absorbed by our atmosphere). At what rate does the sun emit light energy? (The earth-sun distance = 1.5 × 10⁸ km and the earth's 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 23

A standing wave is oscillating at 690 Hz on a string, as shown in the figure. What is the speed of traveling waves on this string?

A) 280 m/s
B) 410 m/s
C) 210 m/s
D) 140 m/s

Question 24

Observer A is 3.0 m from a tiny light bulb and observer B is 12.0 m from the same bulb. Assume that the light spreads out uniformly and undergoes no significant reflections or absorption. If observer B sees a light of intensity I, the light intensity that A sees is

A) I.
B) 9I.
C) 16I.
D) 36I.
E) 144I.

Question 25

A thin 2.00-m string of mass 50.0 g is fixed at both ends and under a tension of 70.0 N. If it is set into small-amplitude oscillation, what is the frequency of the first harmonic mode?

A) 6.61 Hz
B) 13.2 Hz
C) 26.5 Hz
D) 52.9 Hz

Question 26

A guitar string 0.650 m long has a tension of 61.0 N and a mass per unit length of 3.00 g/m.
(a) What is the speed of waves on the string when it is plucked?
(b) What is the string's fundamental frequency of vibration when plucked?

Question 27

A tiny vibrating source sends waves uniformly in all directions. An area of 3.25 cm² on a sphere of radius 2.50 m centered on the source receives energy at a rate of 4.20 J/s.
(a) What is the intensity of the waves at 2.50 m from the source and at 10.0 m from the source?
(b) At what rate is energy leaving the vibrating source of the waves?

Question 28

A heavy stone of mass m is hung from the ceiling by a thin 8.25-g wire that is 65.0 cm long. When you gently pluck the upper end of the wire, a pulse travels down the wire and returns 7.84 ms later, having reflected off the lower end. The stone is heavy enough to prevent the lower end of the wire from moving. What is the mass m of the stone?

A) 8.90 kg
B) 23.1 kg
C) 35.6 kg
D) 227 kg
E) 349 kg

Question 29

You and your surfing buddy are waiting to catch a wave a few hundred meters off the beach. The waves are conveniently sinusoidal, and you notice that when you're on the top of one wave and moving toward your friend, she is exactly halfway between you and the trough of the wave. 1.50 seconds later, your friend is at the top of the wave. You estimate the horizontal distance between you and your friend at 8.00 m.
(a) What is the frequency of the waves?
(b) Find the speed of the waves.

Question 30

A 8.0-m long wire with a mass of 10 g is under tension. A transverse wave for which the frequency is 570 Hz, the wavelength is 0.10 m, and the amplitude is 3.7 mm is propagating on the wire. The maximum transverse acceleration of a point on a wire is closest to

A) 47,000 m/s².
B) 41,000 m/s².
C) 35,000 m/s².
D) 29,000 m/s².
E) 53,000 m/s².

Question 31

A platinum wire that is 1.20 m long has a radius of 0.500 mm and is fixed at both ends. In its third harmonic it vibrates at 512 Hz. The density of platinum is 21.4 × 10³ kg/m³. What is the tension in the wire?

A) 4.00 kN
B) 2.00 kN
C) 2.82 kN
D) 1.41 kN
E) 1.00 kN

Question 32

A 6.00-m long rope is under a tension of 600 N. Waves travel along this rope at 40.0 m/s. What is the mass of the rope?

A) 1.00 kg
B) 1.25 kg
C) 2.25 kg
D) 2.50 kg
E) 1.12 kg

Question 33

Two people are talking at a distance of 3.0 m from where you are and you measure the sound intensity as 1.1 × 10^-7 W/m². Another student is 4.0 m away from the talkers. What sound intensity does the other student measure? Assume that the sound spreads out uniformly and undergoes no significant reflections or absorption.

A) 6.2 × 10-8 W/m²
B) 1.5 × 10-7 W/m²
C) 8.3 × 10-8 W/m²
D) 7.8 × 10-7 W/m²
E) 2.5 × 10-8 W/m²

Question 34

A 2.0-m string is fixed at both ends and tightened until the wave speed is 78m/s. What is the frequency of the standing wave shown in the figure?

A) 120 Hz
B) 230 Hz
C) 350 Hz
D) 470 Hz

Question 35

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 36

Waves travel along a 100-m length of string which has a mass of 55 g and is held taut with a tension of 75 N. What is the speed of the waves?

A) 3700 m/s
B) 370 m/s
C) 37 m/s
D) 0.37 m/s
E) 3.7 m/s

Question 37

A 2.00-m long piano wire with a mass per unit length of 12.0 g/m is under a tension of 8.00 kN. What is the frequency of the fundamental mode of vibration of this wire?

A) 204 Hz
B) 102 Hz
C) 408 Hz
D) 510 Hz
E) 153 Hz

Question 38

A thin taut string is fixed at both ends and stretched along the horizontal x-axis with its left end at x = 0. It is vibrating in its third OVERTONE, and the equation for the vertical displacement of any point on the string is y(x,t) = (1.22 cm) sin[(14.4 m^-1)x] cos[(166 rad/s)t].
(a) What are the frequency and wavelength of the fundamental mode of this string?
(b) How long is the string?
(c) How fast do waves travel on this string?

Question 39

A 6.0-m wire with a mass of 50 g, is under tension. A transverse wave, for which the frequency is 810 Hz, the wavelength is 0.40 m, and the amplitude is 4.0 mm, is propagating on the wire. The time for a crest of this wave to travel the length of the wire is closest to

A) 19 ms.
B) 16 ms.
C) 21 ms.
D) 23 ms.
E) 25 ms.

Question 40

Calculate the light intensity 1.51 m from a light bulb that emits 100 W of visible light, assuming that the light radiates uniformly in all directions.

A) 3.49 W/m²
B) 4.01 W/m²
C) 43.9 W/m²
D) 50.5 W/m²

Question 41

Two violinists are trying to tune their instruments in an orchestra. One is producing the desired frequency of 440.0 Hz. The other is producing a frequency of 448.4 Hz. By what percentage should the out-of-tune musician change the tension in his string to bring his instrument into tune at 440.0 Hz?

A) +1.9%
B) -1.9%
C) +3.7%
D) -3.7%
E) +8.4%

Question 42

A heavy stone of mass m is hung from the ceiling by a thin 8.25-g wire that is 65.0 cm long. When you gently pluck the upper end of the wire, a pulse travels down the wire and returns 7.84 ms later, having reflected off the lower end. The speed of sound in the room is 344 m/s, and the stone is heavy enough to prevent the lower end of the wire from moving. If the wire is vibrating in its second overtone, what is the frequency of the sound it will produce?

A) 128 Hz
B) 191 Hz
C) 255 Hz
D) 383 Hz
E) 765 Hz

Question 43

Standing waves of frequency 57 Hz are produced on a string that has mass per unit length 0.0160 kg/m. With what tension must the string be stretched between two supports if adjacent nodes in the standing wave are to be 0.71 meters apart?

Question 44

A heavy stone of mass m is hung from the ceiling by a thin 8.25-g wire that is 65.0 cm long. When you gently pluck the upper end of the wire, a pulse travels down the wire and returns 7.84 ms later, having reflected off the lower end. The speed of sound in the room is 344 m/s, and the stone is heavy enough to prevent the lower end of the wire from moving. If the wire is vibrating in its second overtone, what is the wavelength of the sound it will produce?

A) 0.217 m
B) 0.433 m
C) 0.650 m
D) 0.899 m
E) 1.35 m