Deck 16: Superposition and Standing Waves

Question 1

A violin with string length 32 cm and string density 1.5 g/cm resonates with the first overtone of an organ pipe with one end closed.The pipe length is 2 m.What is the tension in the string?

A)1000 N
B)110 N
C)450 N
D)4100 N
E)56 N

Answer 1

1000 N

Question 2

Two stereo speakers mounted 4.52 m apart on a wall emit identical sound waves.You are standing at the opposite wall of the room at a point directly between the two speakers.You walk 2.11 m parallel to the wall,to a location where you first notice that the sound intensity is much less.If the wall along which you are walking is 10.7 m from the wall with the speakers,what is the wavelength of the sound waves?

A)1.71 m
B)2.05 m
C)2.57 m
D)2.91 m

Answer 2

1.71 m

Question 3

A simple harmonic wave described by the equation y(t)= 0.54 cos(3.1x - 2.3t)reflects from both ends of a string that is clamped at each end,resulting in a standing wave that is the sum of y(t)and its reflection.What is the amplitude of the standing wave at x = 0.22 m? The quantities x and y are in meters,and t is in seconds.

A)0.84 m
B)0.57 m
C)0.67 m
D)0.77 m

Answer 3

0.84 m

Question 4

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

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

Question 5

A 4.0 g string,0.39 m long,is under tension.The string produces a 600 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 SI units,is closest to:

A)250
B)200
C)160
D)290
E)340

Question 6

Two harmonic waves of the same frequency and phase but of different amplitudes move in opposite directions on a string.A periodic series of maxima and minima on the string are observed.What is the ratio of the maximum displacement at a minimum position to that at a maximum position,if one amplitude is 52% of the other? (This is called the standing wave ratio. )

A)0.32%
B)48%
C)0.0%
D)52%

Question 7

A string,0.13 m long,vibrating in the n = 4 harmonic,excites an open pipe,0.88 m long,into second overtone resonance.The speed of sound in air is 345 m/s.The velocity of transverse waves in the string,in SI units,is closest to:

A)38
B)36
C)34
D)32
E)30

Question 8

A guitar-like stringed instrument has a string that is 20 cm long.It sounds the musical note A (440 Hz)when played without fingering.How far from the end of the string should you place your finger to play the note C (523 Hz)?

A)3.2 cm
B)2.1 cm
C)4.2 cm
D)5.2 cm

Question 9

Current in a wire is reflected from an unconnected end (to ground)in the same way that sound reflects from an open pipe.If a 500.0 cm wire is excited by a 22.0 MHz oscillator in its lowest mode,what is the ratio of the current speed to that of light?

A)0.49
B)0.37
C)0.73
D)0.092

Question 10

A string,0.26 m long,vibrating in the n = 6 harmonic,excites an open pipe,0.88 m long,into second overtone resonance.The speed of sound in air is 345 m/s.The common resonant frequency of the string and the pipe,in SI units,is closest to:

A)590
B)390
C)490
D)690
E)760

Question 11

A string,0.15 m long,vibrating in the n = 5 harmonic,excites an open pipe,0.82 m long,into second overtone resonance.The speed of sound in air is 345 m/s.The distance between a node and an adjacent antinode,in the string,in mm,is closest to:

A)15
B)7.5
C)23
D)30
E)150

Question 12

A 0.588 m string is clamped at both ends.If the lowest standing wave frequency in the string is 326 Hz,what is the wave speed?

A)383 m/s
B)475 m/s
C)582 m/s
D)724 m/s

Question 13

A 2.0 g string,0.67 m long,is under tension.The string produces a 700 Hz tone when it vibrates in the third harmonic.The speed of sound in air is 344 m/s.The wavelength of the tone in air,in SI units,is closest to:

A)0.49
B)0.55
C)0.61
D)0.67
E)0.45

Question 14

If the frequency of a violin string is to be increased by 20%,what change in tension must be applied?

A)44%
B)20%
C)4.5%
D)10%

Question 15

A string,2.0 meters in length,is fixed at both ends and tightened until the wave speed is 78 m/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 16

Situation 16.1
A standing wave of the third overtone is induced in a stopped pipe,1.2 m long.The speed of sound is 340 m/s.
In Situation 16.1,the number of antinodes in the standing wave pattern is:

A)3
B)4
C)5
D)6
E)7

Question 17

Two motors in a factory are running at slightly different rates.One runs at 825 rpm and the other at 786 rpm.You hear the sound intensity increase and then decrease periodically due to wave interference.How long does it take between successive instances of the sound intensity increasing?

A)1.54 s
B)1.43 s
C)1.66 s
D)1.79 s

Question 18

An open organ pipe is tuned to a given frequency.A second pipe with both ends open resonates with twice this frequency.What is the ratio of the length of the first pipe to the second pipe?

A)1
B)2
C)4
D).5

Question 19

A 4.0 g string,0.36 m long,is under tension.The string produces a 500 Hz tone when it vibrates in the third harmonic.The speed of sound in air is 344 m/s.In this situation,the wavelength of the standing wave in the string,in SI units,is closest to:

A)0.24
B)0.36
C)0.54
D)0.72
E)0.90

Question 20

A 500.0 cm rope under a tension of 70.0 N.is set into oscillation.The mass density of the rope is 120.0 g/cm.What is the frequency of the first harmonic mode (m = 2)?

A)0.48 Hz
B)2.92 Hz
C)0.0048 Hz
D)0.153 Hz

Question 21

Two speakers next to each other oscillate in phase,one at 404 Hz and the other at 400 Hz.If you stand in front of them,you will hear a sound of frequency 402 Hz that fluctuates between loud and soft with a frequency of 4 Hz.

Question 22

A string 2.0 m long and fixed at both ends is vibrating in its fourth harmonic in a room at 20C.The wavelength of the sound it produces is 1.0 m.

Question 23

An open pipe,0.92 m long,vibrates in the second overtone with a frequency of 584 Hz.In this situation,the speed of sound in air,in SI units,is closest to:

A)358
B)349
C)353
D)344
E)363

Question 24

If a tube filled with air and closed at both ends is 1.60 m long,the longest possible wavelength of the standing waves in this tube is 1.60 m.

Question 25

A gamma ray (a pulse of electromagnetic energy)has a frequency of 2.42 $\times$ 10²⁰ Hz.What is the ratio of its wavelength to the radius of the nucleus which produced it (radius = 5.0 $\times$ 10^-13 cm)?

A)248
B)39.4
C)1.21 × 10⁸
D)0.015

Question 26

A guitar string is fixed at both ends.If you tighten it to increase its tension,the frequencies of its normal modes will increase but its wavelengths will not be affected.

Question 27

An open pipe,0.95 m long,vibrates in the second overtone with a frequency of 561 Hz.In this situation,the distance from the center of the pipe to the nearest antinode,in cm,is closest to:

A)16
B)7.9
C)24
D)32
E)zero

Question 28

A guitar string 0.65 m long has a tension of 61 N and a mass per unit length of 3.0 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?
(c)What other frequencies will this string allow?

Question 29

If one speaker emits a wave crest at the same time that another one emits a wave trough,these speakers are π/2 out of phase with each other.

Question 30

Situation 16.1
A standing wave of the third overtone is induced in a stopped pipe,1.2 m long.The speed of sound is 340 m/s.
In Situation 16.1,the frequency of the sound produced by the pipe,in SI units,is closest to:

A)210
B)280
C)350
D)430
E)500

Question 31

The tension in each of two strings is adjusted so that both vibrate at exactly 666 Hz.The tension in one of the strings is then increased slightly.As a result,six beats per second are heard when both strings vibrate.What is the new frequency of the string that was tightened?

A)672 Hz
B)660 Hz
C)669 Hz
D)663 Hz

Question 32

To demonstrate interference of sound waves,a buzzer is placed in the center of an empty mailing tube that is 0.80 m long.The sound waves emerge from the two ends of the tube in phase and interfere with each other in the region surrounding the tube.When you stand 4.0 m directly in front of the tube,equidistant from its two ends,you hear a loud sound.If you then move parallel to the tube a distance of 1.3 m,the sound nearly disappears.
(a)What's the wavelength of the buzzer's sound waves?
(b)What's the buzzer's frequency? (Assume the speed of sound in air is 340 m/s. )

Question 33

A 0.335 m string is clamped at both ends.If the lowest standing wave frequency in the string is 326 Hz,what is the wave speed?

A)218 m/s
B)270 m/s
C)331 m/s
D)412 m/s

Question 34

The sound from two loudspeakers is received by a microphone at a point far away along the line through the speakers.The microphone registers maximum intensity when the speakers are 20 cm apart.The sound intensity decreases as the distance between the speakers is increased,reaching zero at a separation of 91 cm.If the distance between the speakers continues to increase,at what separation will the sound intensity again be a maximum?

A)162 cm
B)172 cm
C)182 cm
D)192 cm

Question 35

If the fourth harmonic for a string fixed at both ends is 220 Hz,the fundamental frequency for this string is 880 Hz.

Question 36

You press two flat pieces of glass together so that a very thin layer of air is trapped between them.Incoming light can reflect from the boundary between the top glass plate and the air,and also from the boundary between the air and the bottom plate;the two reflected waves can then interfere with each other.What is the smallest spacing between the plates that will produce a strong reflection when red light of 680 nm wavelength shines perpendicularly on them?

Question 37

Two loudspeakers placed 6.0 m apart are driven in phase by an audio oscillator,whose frequency range is 1595 Hz to 2158 Hz.A point P is located 4.7 m from one loudspeaker and 3.6 m from the other.The speed of sound is 344 m/s.The frequency produced by the oscillator,for which destructive interference occurs at point P,in SI units,is closest to:

A)2033
B)2127
C)2095
D)2064
E)2001

Question 38

A string fixed at both ends that is vibrating in its eighth harmonic will have 8 antinodes and 9 nodes.

Question 39

Radio station KBOB broadcasts at a frequency of 85.7 MHz on your dial.Since nearly all of the station's audience is due south of the transmitter,the managers of KBOB don't want to waste any energy broadcasting to the east and west.They decide to build two towers,transmitting at exactly the same frequency,aligned on an east-west axis.For engineering reasons,the two towers must be at least 10 meters apart.What's the shortest distance between the towers that will eliminate all broadcast power to the east and west?

Question 40

Calculate the light intensity 1.45 m from a 100.0 W light bulb.Assume that the light radiates equally in all directions.

A)3.79 W/m²
B)4.36 W/m²
C)47.6 W/m²
D)54.7 W/m²

Question 41

A thin film of refractive index 1.40 covers a flat sheet of glass of refractive index 1.50.If light of wavelength 600 nm strikes the film from air perpendicular to its surface,the minimum film thickness needed to cause destructive interference in the reflected light is 150 nm.

Question 42

A tube open at one end and closed at the other produces sound of fundamental frequency of 350 Hz.If you now open the closed end,the fundamental frequency becomes 175 Hz.

Question 43

Which of the following is an accurate statement?

A)A system like a vibrating string has only one possible frequency.
B)In order for a singer to break a wine glass by singing,she must adjust the amplitude of the sound she makes so that it is exactly equal to the amplitude of vibration of the wine glass.
C)The fundamental frequency of a system is the name given to the highest possible frequency at which the system will naturally vibrate.
D)The sound in an organ pipe can vibrate at an infinite number of frequencies.

Question 44

When a guitar is tuned,what is it that is changed?

A)The wavelength of the fundamental.
B)The frequency of the fundamental.
C)The amplitude of the fundamental.

Question 45

In the figure above,some wavefronts are emitted by a source of sound S.This picture can help us to understand

A)why the siren on a police car changes its pitch as it races past us.
B)why a sound grows quieter as we move away from the source.
C)how sonar works.
D)the phenomenon of beats.
E)why it is that our hearing is best near 3000 Hz.