Deck 17: Waves II

Question 1

The longitudinal displacement of a mass element in a medium as a sound wave passes through it is given by s = s_m cos (kx - ωt). Consider a sound wave of frequency 440 Hz and wavelength 0.75m. If s_m = 12 µm, what is the displacement of an element of air located at x = 1.2 m at time t = 0.11 s?

A) 3.7 µm
B) 4.9 µm
C) 6.0 µm
D) 8.2 µm
E) 12 µm

Answer 1

3.7 µm

Question 2

Two small identical speakers are connected (in phase) to the same source. The speakers are 3 m apart and at ear level. An observer stands at X, 4 m in front of one speaker as shown. The sound she hears will be most intense if the wavelength is:

A) 5 m
B) 4 m
C) 3 m
D) 2 m
E) 1 m

Answer 2

1 m

Question 3

This graph shows the position of an element of air as a function of time as a sound wave passes through it. Which letter corresponds to the amplitude of the wave?

A) A
B) B
C) C
D) D
E) E

Answer 3

D

Question 4

Take the speed of sound to be 340 m/s. A thunder clap is heard about 3 s after the lightning is seen. The source of both light and sound is:

A) moving overhead faster than the speed of sound
B) emitting a much higher frequency than is heard
C) emitting a much lower frequency than is heard
D) about 1000 m away
E) much more than 1000 m away

Question 5

The difference between transverse and longitudinal waves:

A) depends on the frequency of the wave
B) depends on the wavelength of the wave
C) depends on the direction of propagation of the wave
D) depends on the direction of oscillation of the medium relative to the direction of propagation of the wave
E) there is no difference, they are just two ways of describing the same phenomenon

Question 6

Two waves are out of phase by half a wavelength. What is this in radians?

A) π/6
B) π/4
C) π/2
D) π
E) 3π/2

Question 7

A fire whistle emits a tone of 170 Hz. Take the speed of sound in air to be 340 m/s. The wavelength of this sound is about:

A) 0.5 m
B) 1.0 m
C) 2.0 m
D) 3.0 m
E) 340 m

Question 8

This graph shows the position of an element of air as a function of time as a sound wave passes through it. Which letter corresponds to the period of the wave?

A) A
B) B
C) C
D) D
E) E

Question 9

The longitudinal displacement of a mass element in a medium as a sound wave passes through it is given by s = s_m cos (kx - ωt). Consider a sound wave of frequency 440 Hz and wavelength 0.75m. If s_m = 12 µm, how long does it take an element of air to move from a displacement of 12 µm to a displacement of 0 µm?

A) 0.57 ms
B) 1.1 ms
C) 2.3 ms
D) 3.4 ms
E) 4.6 ms

Question 10

Two sound waves are traveling through the same medium. They have the same amplitude, wavelength, and direction of travel. If the phase difference between them is 7π, the type of interference they exhibit is:

A) fully constructive
B) fully destructive
C) indeterminate
D) partially constructive
E) partially destructive

Question 11

At points in a sound wave where the gas is maximally compressed, the pressure

A) is a maximum
B) is a minimum
C) is equal to the ambient value
D) is greater than the ambient value but less than the maximum
E) is less than the ambient value but greater than the minimum

Question 12

Two small identical speakers are connected (in phase) to the same source. The speakers are 3 m apart and at ear level. An observer stands at X, 4 m in front of one speaker as shown. If the amplitudes are not changed, the sound he hears will be least intense if the wavelength is:

A) 1 m
B) 2 m
C) 3 m
D) 4 m
E) 5 m

Question 13

What is a wavefront?

A) A set of points on a wave that are all traveling in the same direction.
B) The front of the wave is the highest point on the wave.
C) The front of the wave faces the direction the wave is traveling.
D) A set of points on a wave that all have the same wavelength.
E) A set of points on a wave that all have the same displacement.

Question 14

Which of the following properties of a sound wave determine its "pitch"?

A) amplitude
B) distance form source to detector
C) frequency
D) phase
E) speed

Question 15

The speed of sound in air is 340 m/s, and the density of air is 1.2 kg/m³. If the displacement amplitude of a 440-Hz sound wave is 10 µm, what is its pressure-variation amplitude?

A) 1.8 Pa
B) 3.3 Pa
C) 11 Pa
D) 15 Pa
E) 28 Pa

Question 16

The bulk modulus of water is 2.2 x 10⁹ Pa, and its density is 1.0 x 10³ kg/m³. What is the speed of sound in water?

A) 1.5 x 10³ m/s
B) 2.2 x 10³ m/s
C) 3.5 x 10³ m/s
D) 4.5 x 10³ m/s
E) 2.2 x 10⁶ m/s

Question 17

A sound wave has a wavelength of 3.0 m. The distance from a compression center to the adjacent rarefaction center is:

A) 0.75 m
B) 1.5 m
C) 3.0 m
D) need to know wave speed
E) need to know frequency

Question 18

The speed of a sound wave is determined by:

A) its amplitude
B) its intensity
C) its pitch
D) number of overtones present
E) the transmitting medium

Question 19

During a time interval of exactly one period of vibration of a tuning fork, the emitted sound travels a distance:

A) equal to the length of the tuning fork
B) equal to twice the length of the tuning fork
C) of about 330 m
D) which decreases with time
E) of one wavelength in air

Question 20

Two waves are out of phase by half a wavelength. What is this in degrees?

A) 45°
B) 90°
C) 135°
D) 180°
E) 360°

Question 21

The intensity of sound wave A is 100 times that of sound wave B. Relative to wave B the sound level of wave A is:

A) -2 db
B) +2 db
C) +10 db
D) +20 db
E) +100 db

Question 22

Consider two imaginary spherical surfaces of different radius, both centered on a point sound source emitting spherical waves. The power transmitted across the larger sphere is ________ the power transmitted across the smaller and the intensity at a point on the larger sphere is ________ the intensity at a point on the smaller.

A) greater than, the same as
B) greater than, greater than
C) greater than, less than
D) the same as, less than
E) the same as, the same as

Question 23

Two pipes are each open at one end and closed at the other. Pipe A has length L and pipe B has length 2L. Which harmonic of pipe B matches in frequency the fundamental of pipe A?

A) The fundamental
B) The second
C) The third
D) The fourth
E) There are none

Question 24

The sound level at a point P is 14 db below the sound level at a point 1.0 m from a point source. Assuming the intensity from a point source drops off like the inverse square of the distance, the distance from the source to point P is:

A) 4.0 cm
B) 20 m
C) 2.0 m
D) 5.0 m
E) 25 m

Question 25

A 1024 Hz tuning fork is used to obtain a series of resonance levels in a gas column of variable length, with one end closed and the other open. The length of the column changes by 20 cm from resonance to resonance. From this data, the speed of sound in this gas is:

A) 20 m/s
B) 51 m/s
C) 102 m/s
D) 205 m/s
E) 410 m/s

Question 26

The intensity of a certain sound wave is 6 $\mu$ W/cm². If its intensity is raised by 10 decibels, the new intensity is:

A) 60 $\mu$ W/cm²
B) 6.6 $\mu$ W/cm²
C) 6.06 $\mu$ W/cm²
D) 600 $\mu$ W/cm²
E) 12 $\mu$ W/cm²

Question 27

A microphone of surface area 2.0 cm² absorbs 1.1 mW of sound. What is the intensity of sound hitting the microphone?

A) 2.2 x 10^-5 W/m²
B) 0.55 W/m²
C) 2.2 W/m²
D) 2.8 W/m²
E) 5.5 W/m²

Question 28

The speed of sound in air is 340 m/s, and the density of air is 1.2 kg/m³. If the displacement amplitude of a 440-Hz sound wave is 10 µm, what is the intensity of the wave?

A) 0.16 W/m²
B) 0.32 W/m²
C) 12 W/m²
D) 16 W/m²
E) 32 W/m²

Question 29

If I₀ = 10^-12 W/m², and I = 4.5 x 10^-8 W/m², what is log (I/I₀)?

A) 4.5 x 10⁴
B) 18
C) 11
D) 4.7
E) 3.7

Question 30

An organ pipe with one end open and the other closed is operating at one of its resonant frequencies. The open and closed ends are respectively:

A) pressure node, pressure node
B) pressure node, displacement node
C) displacement antinode, pressure node
D) displacement node, displacement node
E) pressure antinode, pressure antinode

Question 31

A tuning fork produces sound waves of wavelength $\lambda$ in air. This sound is used to cause resonance in an air column, closed at one end and open at the other. The length of this column CANNOT be:

A) $\lambda$ /4
B) 2 $\lambda$ /4
C) 3 $\lambda$ /4
D) 5 $\lambda$ /4
E) 7 $\lambda$ /4

Question 32

An organ pipe with one end closed and the other open has length L. Its fundamental frequency is proportional to:

A) L
B) 1/L
C) 1/L²
D) L²
E)

Question 33

If the sound level is increased by 10 db the intensity increases by a factor of:

A) 2
B) 5
C) 10
D) 20
E) 100

Question 34

The "A" on a trumpet and a clarinet have the same pitch, but the two are clearly distinguishable. Which property is most important in enabling one to distinguish between these two instruments?

A) intensity
B) fundamental frequency
C) displacement amplitude
D) pressure amplitude
E) harmonic content

Question 35

The standard reference sound level is about:

A) the threshold of human hearing at 1000 Hz
B) the threshold of pain for human hearing at 1000 Hz
C) the level of sound produced when the 1 kg standard mass is dropped 1 m onto a concrete floor
D) the level of normal conversation
E) the level of sound emitted by a standard 60 Hz tuning fork

Question 36

The sound intensity 5.0 m from point source is 0.50 W/m². The power output of the source is:

A) 12.5 W
B) 39 W
C) 79 W
D) 160 W
E) 260 W

Question 37

A column of argon is open at one end and closed at the other. The shortest length of such a column that will resonate with a 200 Hz tuning fork is 42.5 cm. The speed of sound in argon must be:

A) 85.0 m/s
B) 170 m/s
C) 340 m/s
D) 470 m/s
E) 940 m/s

Question 38

A vibrating tuning fork is held over a water column with one end closed and the other open. As the water level is allowed to fall, a loud sound is heard for water levels separated by 17 cm. If the speed of sound in air is 340 m/s, the frequency of the tuning fork is:

A) 58 Hz
B) 500 Hz
C) 1000 Hz
D) 2000 Hz
E) 5800 Hz

Question 39

A standing wave in a pipe has nodes that are 1.2 m apart. What is the wavelength of the wave?

A) 0.6 m
B) 1.2 m
C) 1.8 m
D) 2.4 m
E) cannot tell without knowing which harmonic it is

Question 40

You are listening to an "A" note played on a violin string. Let the subscript "s" refer to the violin string and "a" refer to the air. Then:

A) f_s = f_a but $\lambda$ _s $\neq$$\lambda$ _a
B) f_s = f_a and $\lambda$ _s = $\lambda$ 0_a
C) $\lambda$ _s = $\lambda$ _a but f_s $\neq$ f_a
D) $\lambda$ _s $\neq$$\lambda$ _a and f_s $\neq$ f_a
E) linear density of string = volume density of air

Question 41

To produce beats it is necessary to use two waves:

A) traveling in opposite directions
B) of slightly different frequencies
C) of equal wavelengths
D) of equal amplitudes
E) whose ratio of frequencies is an integer

Question 42

The largest number of beats per second will be heard from which pair of tuning forks?

A) 200 and 201 Hz
B) 256 and 260 Hz
C) 534 and 540 Hz
D) 763 and 774 Hz
E) 8420 and 8422 Hz

Question 43

Five organ pipes are described below. Which one has the highest fundamental frequency?

A) A 2.3-m pipe with one end open and the other closed
B) A 3.3-m pipe with one end open and the other closed
C) A 1.6-m pipe with both ends open
D) A 3.0-m pipe with both ends open
E) a pipe in which the displacement nodes are 5 m apart

Question 44

Two identical strings, A and B, have nearly the same tension. When they both vibrate in their fundamental resonant modes, there is a beat of 3 Hz. When string B is tightened slightly, to increase the tension, the beat frequency becomes 6 Hz. This means:

A) that before tightening A had a higher frequency than B, but after tightening, B has a higher frequency than A
B) that before tightening B had a higher frequency than A, but after tightening, A has a higher frequency than B
C) that before and after tightening A has a higher frequency than B
D) that before and after tightening B has a higher frequency than A
E) none of the above

Question 45

If the speed of sound is 340 m/s, the two lowest frequencies of an 0.5 m organ pipe, closed at one end, are approximately:

A) 170 and 340 Hz
B) 170 and 510 Hz
C) 340 and 680 Hz
D) 340 and 1020 Hz
E) 57 and 170 Hz

Question 46

Two stationary tuning forks (350 and 352 Hz) are struck simultaneously. The resulting sound is observed to:

A) beat with a frequency of 2 beats/s
B) beat with a frequency of 351 beats/s
C) be loud but not beat
D) be Doppler shifted by 2 Hz
E) have a frequency of 702 Hz

Question 47

Organ pipe Y (open at both ends) is twice as long as organ pipe X (open at one end) as shown. The ratio of their fundamental frequencies f_X::f_Y is:

A) 1:1
B) 1:2
C) 2:1
D) 1:4
E) 4:1

Question 48

Two identical tuning forks vibrate at 256 Hz. One of them is then loaded with a drop of wax, after which 6 beats per second are heard. The frequency of the loaded tuning fork is:

A) 250 Hz
B) 253 Hz
C) 256 Hz
D) 259 Hz
E) 262 Hz

Question 49

The rise in pitch of an approaching siren is an apparent increase in its:

A) speed
B) amplitude
C) frequency
D) wavelength
E) number of overtones

Question 50

If the speed of sound is 340 m/s, the shortest pipe, closed at one end, which resonates at 218 Hz is:

A) 39 cm
B) 78 cm
C) 1.6 m
D) 3.1 m
E) 6.2 m

Question 51

The lowest tone produced by a certain organ comes from a 3.0-m pipe with both ends open. If the speed of sound is 340 m/s, the frequency of this tone is approximately:

A) 14 Hz
B) 28 Hz
C) 57 Hz
D) 110 Hz
E) 230 Hz

Question 52

A stationary source generates 5.0 Hz water waves whose speed is 2.0 m/s. A boat is approaching the source at 1.0 m/s. The frequency of these waves, as observed by a person in the boat, is:

A) 2.5 Hz
B) 5.0 Hz
C) 7.5 Hz
D) 15 Hz
E) 30 Hz

Question 53

The Doppler shift formula for the frequency detected is where f ' is the frequency emitted, v is the speed of sound, v_D is the speed of the detector, and v_s is the speed of the source. Suppose the source is traveling at 5 m/s away from the detector, the detector is traveling at 7 m/s toward the source, and there is a 3 m/s wind blowing from the source toward the detector. The values that should be substituted into the Doppler shift equation are:

A) v_D = 7 m/s and v_s = 5 m/s
B) v_D = 10 m/s and v_s = 8 m/s
C) v_D = 4 m/s and v_s = 2 m/s
D) v_D = 10 m/s and v_s = 2 m/s
E) v_D = 4 m/s and v_s = 8 m/s

Question 54

When listening to tuning forks of frequency 256 Hz and 260 Hz, one hears the following number of beats per second:

A) 0
B) 2
C) 4
D) 8
E) 258

Question 55

In order for two sound waves to produce audible beats, it is essential that the two waves have:

A) the same amplitude
B) the same frequency
C) the same number of overtones
D) slightly different amplitudes
E) slightly different frequencies

Question 56

The valves of a trumpet and the slide of a trombone are for the purpose of:

A) playing short (staccato) notes
B) tuning the instruments
C) changing the harmonic content
D) changing the length of the air column
E) producing gradations in loudness

Question 57

The speed of sound in air is 340 m/s. The shortest air column, closed at one end, which will resonate to a 512 Hz tuning fork is approximately:

A) 4.2 cm
B) 8.3 cm
C) 17 cm
D) 33 cm
E) 66 cm

Question 58

Beats in sound occur when:

A) two waves of the same frequency interfere
B) two waves of slightly different frequency interfere
C) a reflected wave interferes with an incident wave
D) waves travel in two media having slightly different sound velocities
E) source and observer are in relative motion

Question 59

A 200-cm organ pipe with one end open is in resonance with a sound wave of wavelength 270 cm. The pipe is operating in its:

A) fundamental frequency
B) first harmonic
C) second harmonic
D) third harmonic
E) fourth harmonic

Question 60

An organ pipe with both ends open is 0.85 m long. Assuming that the speed of sound is 340 m/s, the frequency of the third harmonic of this pipe is:

A) 200 Hz
B) 300 Hz
C) 400 Hz
D) 600 Hz
E) none of these

Question 61

A stationary source S generates circular outgoing waves on a lake. The wave speed is 5.0 m/s and the crest-to-crest distance is 2.0 m. A person in a motor boat heads directly toward S at 3.0 m/s. To this person, the frequency of these waves is:

A) 1.0 Hz
B) 1.5 Hz
C) 2.0 Hz
D) 4.0 Hz
E) 8.0 Hz

Question 62

A source emits sound with a frequency of 1000 Hz. Both it and an observer are moving in the same direction with the same speed, 100 m/s. If the speed of sound is 340 m/s, the observer hears sound with a frequency of:

A) 290 Hz
B) 540 Hz
C) 1000 Hz
D) 1800 Hz
E) 3400 Hz

Question 63

A plane produces a sonic boom only when:

A) its speed changes from being slower than the speed of sound to being faster than the speed of sound
B) it emits sound waves of high frequency
C) it flies at high altitudes
D) it flies on a curved path
E) it flies faster than the speed of sound

Question 64

If the speed of sound is 340 m/s a plane flying at 400 m/s has a Mach number of:

A) 0.85
B) 1.2
C) 1.4
D) 1.7
E) 400

Question 65

A source emits sound with a frequency of 1000 Hz. It is moving at 20 m/s toward a stationary reflecting wall. If the speed of sound is 340 m/s an observer at rest directly behind the source hears a beat frequency of:

A) 3.0 Hz
B) 55 Hz
C) 63 Hz
D) 114 Hz
E) 118 Hz

Question 66

The diagram shows four situations in which a source of sound S and a detector D are either moving or stationary. The arrows indicate the directions of motion. The speeds (when not zero) are all the same. (Note that the detector in situation 3 is stationary). Rank the situations according to the apparent frequency of the source, lowest to highest.

A) 1, 2, 3, 4
B) 4, 3, 2, 1
C) 1, 3, 4, 2
D) 2, 1, 4, 3
E) None of the above

Question 67

If the speed of sound is 340 m/s a plane flying at 400 m/s creates a conical shock wave with an apex half angle of:

A) 0° (no shock wave)
B) 32 $\degree$
C) 40 $\degree$
D) 50 $\degree$
E) 58 $\degree$

Question 68

In each of the following two situations a source emits sound with a frequency of 1000 Hz. In situation I the source is moving at 100 m/s toward an observer at rest. In situation II the observer is moving at 100 m/s toward the source, which is stationary. The speed of sound is 340 m/s. The frequencies heard by the observers in the two situations are:

A) I: 1417 Hz; II: 1294 Hz
B) I: 1417 Hz; II: 1417 Hz
C) I: 1294 Hz; II: 1294 Hz
D) I: 773 Hz; II: 706 Hz
E) I: 773 Hz; II: 773 Hz

Question 69

A stationary source emits a sound wave of frequency f. If it were possible for a man to travel toward the source at the speed of sound, he would observe the emitted sound to have a frequency of:

A) 0
B) f/2
C) 2f/3
D) 2f
E) infinity

Question 70

The speed of sound is 340 m/s. A plane flies horizontally at an altitude of 10,000 m and a speed of 400 m/s. When an observer on the ground hears the sonic boom the horizontal distance from the point on its path directly above the observer to the plane is (assume the speed of sound does not change with altitude):

A) 5800 m
B) 6100 m
C) 8400 m
D) 12,000 m
E) 16,000 m

Question 71

A source emits sound with a frequency of 1000 Hz. It and an observer are moving toward each other, each with a speed of 100 m/s. If the speed of sound is 340 m/s, the observer hears sound with a frequency of:

A) 290 Hz
B) 540 Hz
C) 1000 Hz
D) 1800 Hz
E) 3400 Hz