Deck 11: Waves

Question 1

A string is stretched with a tension of 120 N. The string has a mass of 10.0 grams and has a length of 2.50 meters. The velocity of wave propagation along the string is

A) 125 m/s.
B) 142 m/s.
C) 173 m/s.
D) 185 m/s.
E) 217 m/s.

Answer 1

173 m/s.

Question 2

A string on a guitar is stretched between two points 30.0 cm apart with a tension of 100 N. The mass/length of the string is 0.00300 kg/m. The velocity of wave propagation on the string is

A) 175 m/s.
B) 183 m/s.
C) 205 m/s.
D) 267 m/s.
E) 300 m/s.

Answer 2

183 m/s.

Question 3

A string on a guitar is stretched between two points 35.0 cm apart with a tension of 65.0 N. The mass/length of the string is 0.00400 kg/m. The velocity of wave propagation on the string is

A) 127 m/s.
B) 198 m/s.
C) 210 m/s.
D) 273 m/s.
E) 305 m/s.

Answer 3

127 m/s.

Question 4

What is the distance between a node and an adjacent antinode in a standing wave?

A) wavelength/1
B) wavelength/2
C) wavelength/3
D) wavelength/4

Question 5

Standing waves are produced by the superposition of two waves with

A) the same amplitude, frequency, and direction of propagation.
B) the same amplitude, frequency, and opposite direction of propagation.
C) the same amplitude, different frequencies, and opposite direction of propagation.
D) the same amplitude, different frequencies, and same direction of propagation.

Question 6

What is the distance between adjacent nodes in a standing wave?

A) wavelength/4
B) wavelength/3
C) wavelength/2
D) wavelength/1

Question 7

The intensity of the sound wave from an airplane is 1.0 × 10² W/m² at 5.0 m. What is the intensity at 100 m?

A) 0.25 W/m²
B) 0.53 W/m²
C) 5.0 W/m²
D) 0.25 mW/m²

Question 8

A sound source radiates sound uniformly in all directions. The intensity of the sound at a distance of 100 m is 1.00 × 10⁻⁴ W/m². The power output of the sound source is

A) 12.6 W.
B) 16.2 W.
C) 20.4 W.
D) 24.5 W.
E) 30.6 W.

Question 9

A sound source of power 100 watts radiates sound uniformly in all directions. The intensity of the sound at a distance of 4.00 m is

A) 0.301 W/m².
B) 0.353 W/m².
C) 0.497 W/m².
D) 0.535 W/m².
E) 0.621 W/m².

Question 10

A string on a violin is stretched between two points 20.0 cm apart with a tension of 120 N. The mass/length of the string is 0.00200 kg/m. The frequency of the mode of vibration with the lowest frequency is

A) 502 Hz.
B) 550 Hz.
C) 598 Hz.
D) 612 Hz.
E) 750 Hz.

Question 11

A string on a guitar is stretched between two points 35.0 cm apart with a tension of 65.0 N. The mass/length of the string is 0.00400 kg/m. The frequency of the mode of vibration with the lowest frequency is

A) 315 Hz.
B) 276 Hz.
C) 250 Hz.
D) 205 Hz.
E) 182 Hz.

Question 12

A string on a guitar is stretched between two points 35.0 cm apart with a tension of 65.0 N. The mass/length of the string is 0.00400 kg/m. The wavelength of the mode of vibration with the lowest frequency is

A) 0.5 m.
B) 0.6 m.
C) 0.7 m.
D) 0.8 m.
E) 0.9 m.

Question 13

A string is stretched with a tension of 100 N. The string has a length of 2.00 meters. The velocity of wave propagation along the string is 220 m/s. The mass of the string is

A) 3.75 g.
B) 4.13 g.
C) 4.66 g.
D) 5.21 g.
E) 5.74 g.

Question 14

A string with a length of 1.20 m has a mass of 4.00 g. The velocity of wave propagation along the string is 185 m/s. The tension of the stretched string is

A) 162 N.
B) 145 N.
C) 130 N.
D) 114 N.
E) 102 N.

Question 15

A sound source of power 150 watts radiates sound uniformly in all directions. The intensity of the sound at a distance of 4.00 m is

A) 0.389 W/m².
B) 0.403 W/m².
C) 0.582 W/m².
D) 0.746 W/m².
E) 0.927 W/m².

Question 16

A string on a guitar is stretched between two points 30.0 cm apart with a tension of 100 N. The mass/length of the string is 0.00300 kg/m. The frequency of the mode of vibration with the lowest frequency is

A) 304 Hz.
B) 350 Hz.
C) 376 Hz.
D) 415 Hz.
E) 433 Hz.

Question 17

A string on a guitar is stretched between two points 30.0 cm apart with a tension of 100 N. The mass/length of the string is 0.003 kg/m. The wavelength of the mode of vibration with the lowest frequency is

A) 0.3 m.
B) 0.4 m.
C) 0.5 m.
D) 0.6 m.
E) 0.7 m.

Question 18

A string with a length of 2.50 m has a mass of 5.00 g. The velocity of wave propagation along the string is 210 m/s. The tension of the stretched string is

A) 88.2 N.
B) 75.0 N.
C) 70.2 N.
D) 66.7 N.
E) 60.2 N.

Question 19

A string is stretched with a tension of 120 N. The string has a length of 2.5 meters. The velocity of wave propagation along the string is 220 m/s. The mass per unit length of the string is

A) 5.8 × 10⁻³ kg/m.
B) 5.0 × 10⁻³ kg/m.
C) 4.2 × 10⁻³ kg/m.
D) 3.7 × 10⁻³ kg/m.
E) 2.5 × 10⁻³ kg/m.

Question 20

A string on a violin is stretched between two points 20.00 cm apart with a tension of 120.0 N. The mass/length of the string is 0.002000 kg/m. The frequency of the mode next higher than the fundamental mode is

A) 1,400 Hz.
B) 1,322 Hz.
C) 1,225 Hz.
D) 1,558 Hz.
E) 2,120 Hz.

Question 21

The period of a periodic wave is 2.80 milliseconds. The frequency of the vibration motion of the wave is

A) 450 Hz.
B) 437 Hz.
C) 402 Hz.
D) 357 Hz.
E) 306 Hz.

Question 22

The frequency of a periodic wave is 340 Hz. The period of the vibration motion of the wave is

A) 2.56 milliseconds.
B) 2.94 milliseconds.
C) 3.55 milliseconds.
D) 3.94 milliseconds.
E) 4.25 milliseconds.

Question 23

The speed of waves in stretched string depends on which of the following?

A) the tension in the string
B) the amplitude of the waves
C) the wavelength of the waves
D) the frequency of the waves

Question 24

A string on a violin is stretched between two points 20.00 cm apart with a tension of 120.0 N. The mass/length of the string is 0.002000 kg/m. The frequency of the 2^nd overtone is

A) 1,502 Hz.
B) 1,837 Hz.
C) 2,237 Hz.
D) 2,568 Hz.
E) 3,250 Hz.

Question 25

The frequency of a periodic wave is 325 Hz. If the wavelength is 50.0 cm, then what is the velocity of the wave?

A) 163 m/s
B) 203 m/s
C) 237 m/s
D) 285 m/s
E) 316 m/s

Question 26

The wavelength of a periodic wave is 0.750 m. If the frequency is 365 Hz, then what is the angular frequency ω of the wave?

A) 3.87 × 10³ rad/s
B) 3.10 × 10³ rad/s
C) 2.98 × 10³ rad/s
D) 2.29 × 10³ rad/s
E) 1.75 × 10³ rad/s

Question 27

A transverse wave travels at 190 m/s along the x-axis. If the period of the periodic vibrations of the wave is 2.6 milliseconds, then what is the wavelength of the wave?

A) 25.5 cm
B) 35.4 cm
C) 49.4 cm
D) 50.3 cm
E) 54.4 cm

Question 28

A transverse wave travels at 230.0 m/s along the y-axis. If the frequency of the periodic vibrations of the wave is 390.0 Hz, then what is the wavelength of the wave?

A) 58.97 cm
B) 47.23 cm
C) 40.89 cm
D) 36.76 cm
E) 68.97 cm

Question 29

The wavelength of a periodic wave is 0.750 m. If the frequency is 425 Hz, then what is the velocity of the wave?

A) 210 m/s
B) 276 m/s
C) 319 m/s
D) 410 m/s
E) 472 m/s

Question 30

A transverse wave travels at 250 m/s along the z-axis. If the frequency of the periodic vibrations of the wave is 440 Hz, then what is the wavelength of the wave?

A) 21.9 cm
B) 26.7 cm
C) 35.7 cm
D) 56.8 cm
E) 73.7 cm

Question 31

The wavelength of a periodic wave is 0.750 m. If the frequency is 425 Hz, then what is the angular frequency ω of the wave?

A) 5.44 × 10³ rad/s
B) 5.03 × 10³ rad/s
C) 4.21 × 10³ rad/s
D) 3.76 × 10³ rad/s
E) 2.67 × 10³ rad/s

Question 32

A string with a mass/length of 0.00200 kg/m is stretched between two points with a tension of 120 N. If the fundamental frequency is 440 Hz, then what is the distance between the two points?

A) 17.5 cm
B) 20.3 cm
C) 27.8 cm
D) 30.0 cm
E) 35.0 cm

Question 33

Visible light consists of electromagnetic waves with wavelengths (in air) in the range 400-700 nm. The speed of light in air is 3.0 × 10⁸ m/s. What are the frequencies of visible light?

A) 1.33 × 10¹⁴ Hz to 2.33 × 10¹⁴ Hz
B) 1.33 × 10¹² Hz to 2.33 × 10¹² Hz
C) 4.29 × 10¹² Hz to 7.50 × 10¹² Hz
D) 4.29 × 10¹⁴ Hz to 7.50 × 10¹⁴ Hz

Question 34

Two strings on a violin are stretched between two points 20 cm apart. The tensions of the strings are the same. If the ratio of the frequencies of the fundamental modes is 1.5 to 1.0, then what is the ratio of the mass per lengths in the strings?

A) 0.44
B) 0.80
C) 0.85
D) 0.94
E) 0.78

Question 35

A string with a mass/length of 0.00200 kg/m is stretched between two points with a tension of 115 N. If the distance between the points is changed by 1.0% (keeping the tension and mass per unit length the same), then what is the percentage change of the frequency?

A) 0.50%
B) 0.75%
C) 1.00%
D) 1.25%
E) 1.50%

Question 36

A string with a mass/length of 0.00200 kg/m is stretched between two points with a tension of 120 N. If the fundamental frequency is 660 Hz, then what is the distance between the two points?

A) 17.5 cm
B) 18.6 cm
C) 20.3 cm
D) 26.7 cm
E) 30.0 cm

Question 37

The wavelength of a periodic wave is 0.800 m. If the frequency is 400 Hz, then what is the wavenumber k of the wave?

A) 8.56 m⁻¹
B) 7.85 m⁻¹
C) 7.02 m⁻¹
D) 6.35 m⁻¹
E) 5.98 m⁻¹

Question 38

Two strings on a violin are stretched between two points 20.0 cm apart. The mass per length of the strings are the same. If the ratio of the frequencies of the fundamental modes is 1.5 to 1.0, then what is the ratio of the tensions in the strings?

A) 1.22
B) 1.88
C) 1.00
D) 2.25
E) 1.50

Question 39

A wave travels at 175 m/s along the x-axis. If the period of the periodic vibrations of the wave is 3.00 milliseconds, then what is the wavelength of the wave?

A) 25.5 cm
B) 35.6 cm
C) 42.9 cm
D) 49.5 cm
E) 52.5 cm

Question 40

Of these properties of waves, which one is independent of the others?

A) amplitude
B) period
C) frequency
D) wavelength

Question 41

A transverse periodic wave is represented by the equation z(y, t) = 1.50 cm sin(1,250 rad/s t + 10.0 m⁻¹ y). What is the velocity of the wave?

A) 125 m/s in the + z direction
B) 250 m/s in the − z direction
C) 125 m/s in the + y direction
D) 125 m/s in the − y direction
E) 250 m/s in the − y direction

Question 42

A transverse periodic wave is represented by the equation y(x, t) = 2.50 cm cos(2,500 rad/s t − 15.0 m⁻¹ x). What is the velocity of the wave?

A) 450 m/s in the − y direction
B) 333 m/s in the + y direction
C) 333 m/s in the + x direction
D) 167 m/s in the − x direction
E) 167 m/s in the + x direction

Question 43

A transverse periodic wave is represented by the equation z(y, t) = 1.50 cm sin(1,250 rad/s t + 10.0 m⁻¹ y). What are the wavenumber k and direction of propagation of the wave?

A) 10 m⁻¹; traveling in the + y direction
B) 10 m⁻¹; traveling in the − y direction
C) 20 m⁻¹; traveling in the + z direction
D) 20 m⁻¹; traveling in the − z direction
E) 10 m⁻¹; traveling in the − z direction

Question 44

A longitudinal wave travels on a slinky or any long spring. The wave is represented by the equation z(z, t) = 1.2 cm cos(1800 rad/s t + 60 m⁻¹ z). What are the wavenumber and direction of propagation of the wave?

A) 60 m⁻¹; traveling in the + z direction
B) 60 m⁻¹; traveling in the − z direction
C) 60 m⁻¹; traveling in the + x direction
D) 60 m⁻¹; traveling in the − x direction

Question 45

A transverse periodic wave is represented by the equation y(x, t) = 2.50 cm cos(2,500 rad/s t − 15.0 m⁻¹ x). What are the wavenumber k and direction of propagation of the wave?

A) 15.0 m⁻¹; traveling in the − x direction
B) 15.0 m⁻¹; traveling in the + x direction
C) 30.0 m⁻¹; traveling in the + y direction
D) 30.0 m⁻¹; traveling in the − y direction
E) 45.0 m⁻¹; traveling in the + x direction

Question 46

A transverse periodic wave is represented by the equation z(y, t) = 1.50 cm sin(1,250 rad/s t + 10.0 m⁻¹ y). What is the direction of the velocity of the wave?

A) the x direction
B) the y direction
C) the z direction
D) the t direction

Question 47

A transverse periodic wave is represented by the equation y(z, t) = 2.0 cm sin(1,200 rad/s t − 20.0 m⁻¹ z). Another transverse wave is represented by the equation y(z, t) = 2.0 cm sin(1,200 rad/s t + 20.0 m⁻¹ z). What is the equation that represents the superposition of the two waves?

A) y(z, t) = 4.0 cm sin(1,200 rad/s t − 20.0 m⁻¹ z)
B) y(x, t) = 4.0 cm sin(1,200 rad/s t) cos(20.0 m⁻¹ x)
C) y(x, t) = 4.0 cm cos(1,200 rad/s t) sin(20.0 m⁻¹ x)
D) y(x, t) = 4.0 cm cos(1,200 rad/s t + 20.0 m⁻¹ x)

Question 48

A transverse periodic wave is represented by the equation z(y, t) = 1.50 cm sin(1,250 rad/s t + 10.0 m⁻¹ y). What is the direction of the vibration of the wave?

A) the x direction
B) the y direction
C) the z direction

Question 49

A transverse periodic wave is represented by the equation y(z, t) = 2.0 cm sin(1,200 rad/s t − 20.0 m⁻¹ z). Another transverse wave is represented by the equation y(z, t) = 2.0 cm sin(1,200 rad/s t − 20.0 m⁻¹ z). What is the equation that represents the superposition of the two waves?

A) y(z, t) = 4.0 cm sin(1,200 rad/s t − 20.0 m⁻¹ z)
B) y(x, t) = 4.0 cm sin(1,200 rad/s t) cos(20.0 m⁻¹ x)
C) y(x, t) = 4.0 cm cos(1,200 rad/s t) sin(20.0 m⁻¹ x)
D) y(x, t) = 4.0 cm cos(1,200 rad/s t + 20.0 m⁻¹ x)

Question 50

A transverse periodic wave is represented by the equation y(x, t) = 1.50 cm sin(1,500 rad/s t − 10.0 m⁻¹ x). Another transverse wave is represented by the equation y(x, t) = 1.50 cm sin(1,500 rad/s t + 10.0 m⁻¹ x). What is the equation that represents the superposition of the two waves?

A) y(x, t) = 3.0 cm sin(1,500 rad/s t − 10.0 m⁻¹ x)
B) y(x, t) = 3.0 cm sin(1,500 rad/s t) cos(10.0 m⁻¹ x)
C) y(x, t) = 3.0 cm cos(1,500 rad/s t) sin(10.0 m⁻¹ x)
D) y(x, t) = 3.0 cm sin(1,500 rad/s t + 10.0 m⁻¹ x)

Question 51

A transverse periodic wave is represented by the equation y(x, t) = 1.50 cm sin(1,500 rad/s t − 10.0 m⁻¹ x). Another transverse wave is represented by the equation y(x, t) = 1.50 cm sin(1,500 rad/s t − 10.0 m⁻¹ x). What is the equation that represents the superposition of the two waves?

A) y(x, t) = 3.0 cm sin(1,500 rad/s t − 10.0 m⁻¹ x)
B) y(x, t) = 3.0 cm sin(1,500 rad/s t) cos(10.0 m⁻¹ x)
C) y(x, t) = 3.0 cm cos(1,500 rad/s t) sin(10.0 m⁻¹ x)
D) y(x, t) = 3.0 cm sin(1,500 rad/s t + 10.0 m⁻¹ x)

Question 52

A longitudinal wave travels on a slinky or any long spring. The wave is represented by the equation x(x, t) = 2.1 cm cos(2000 rad/s t − 40 m⁻¹ x). What is the direction of propagation of the wave?

A) the − x direction
B) the + x direction
C) the − y direction
D) the + y direction

Question 53

A transverse periodic wave is represented by the equation y(x, t) = 2.50 cm cos(2,500 rad/s t − 15.0 m⁻¹ x). What is the direction of the vibration of the wave?

A) the z direction
B) the y direction
C) the x direction

Question 54

A longitudinal wave travels on a slinky or any long spring. The wave is represented by the equation x(x, t) = 2.1 cm cos(2000 rad/s t − 40 m⁻¹ x). What is the direction of motion of a point on the spring due to the wave?

A) the ± y direction
B) the ± z direction
C) the ± x direction

Question 55

A transverse periodic wave is represented by the equation z(y, t) = 1.50 cm sin(1,250 rad/s t + 10.0 m⁻¹ y). What is the frequency of the vibration of the wave?

A) 319 Hz
B) 289 Hz
C) 240 Hz
D) 199 Hz
E) 150 Hz

Question 56

A transverse periodic wave is represented by the equation y(x, t) = −1.50 cm sin(1,500 rad/s t − 10.0 m⁻¹ x). Another transverse wave is represented by the equation y(x, t) = +1.50 cm sin(1,500 rad/s t + 10.0 m⁻¹ x). What is the equation that represents the superposition of the two waves?

A) y(x, t) = 3.0 cm sin(1,500 rad/s t − 10.0 m⁻¹ x)
B) y(x, t) = 3.0 cm sin(1,500 rad/s t) cos(10.0 m⁻¹ x)
C) y(x, t) = 3.0 cm cos(1,500 rad/s t) sin(10.0 m⁻¹ x)
D) y(x, t) = 3.0 cm sin(1,500 rad/s t + 10.0 m⁻¹ x)

Question 57

A longitudinal wave travels on a slinky or any long spring. The wave is represented by the equation x(x, t) = 2.10 cm cos(2000 rad/s t + 40.0 m⁻¹ x). What is the velocity of the wave?

A) 50 m/s in the + x direction
B) 50 m/s in the − x direction
C) 0.02 m/s in the + x direction
D) 0.02 m/s in the − x direction

Question 58

The wavelength of a periodic wave is 0.500 m. If the frequency is 400 Hz, then what is the wavenumber k of the wave?

A) 12.6 m⁻¹
B) 14.8 m⁻¹
C) 18.4 m⁻¹
D) 21.0 m⁻¹
E) 25.9 m⁻¹

Question 59

A transverse periodic wave is represented by the equation y(x, t) = 2.50 cm cos(2,500 rad/s t − 15.0 m⁻¹ x). What is the frequency of the vibration of the wave?

A) 490 Hz
B) 467 Hz
C) 422 Hz
D) 398 Hz
E) 302 Hz

Question 60

A transverse periodic wave is represented by the equation y(x, t) = A1 sin(ωt − kx). Another transverse wave is represented by the equation y(x, t) = A2 sin(ωt + kx). What is the equation that represents the superposition of the two waves?

A) y(x, t) = (A1 + A2) sin(ωt) cos(kx) + (+A1 + A2) cos(ωt) sin(kx)
B) y(x, t) = (A1 + A2) sin(ωt) cos(kx) + (−A1 − A2) cos(ωt) sin(kx)
C) y(x, t) = (A1 − A2) sin(ωt) cos(kx) + (−A1 + A2) cos(ωt) sin(kx)
D) y(x, t) = (A1 + A2) sin(ωt) cos(kx) + (−A1 + A2) cos(ωt) sin(kx)

Question 61

Two speakers emit incoherent sound waves into the open air. One of them produces 75W of power. A microphone is placed at a position that is 12m from each speakers, and it receives a total intensity of 0.25W/m². What is the power output of the second speaker?

A) 151 W
B) 377 W
C) Need more info to solve.
D) 38 W

Question 62

Two speakers are driven exactly out of phase with each other at 256 Hz. If a microphone placed on the line between the two speakers, exactly in the middle, detects no sound at all, then what is possibly the distance between the microphone and each speaker? The speed of sound is 340 m/s.

A) 0.75 m
B) 0.38 m
C) Can be any distance at all
D) 1.50 m
E) 0.94 m

Question 63

A wave is represented by the equation y(x, t) = 3.2 cm sin(1000 rad/s t − 50 m⁻¹ x). Another wave, with the same wavelength and frequency, has an amplitude of 4.2 cm. If the two waves interfere constructively, then which equation could represent the superposition of the two waves?

A) y(x, t) = 7.4 cm sin(1000 rad/s t + 50.0 m⁻¹ x)
B) y(x, t) = 1.0 cm sin(1000 rad/s t − 50.0 m⁻¹ x)
C) y(x, t) = 1.0 cm sin(1000 rad/s t + 50.0 m⁻¹ x)
D) y(x, t) = 7.4 cm sin(1000 rad/s t − 50.0 m⁻¹ x)

Question 64

A wave is represented by the equation y(x, t) = 3.2 cm sin(1000 rad/s t − 50 m⁻¹ x). Another wave, with the same wavelength and frequency, has an amplitude of 4.2 cm. If the two waves interfere destructively, then which equation could represent the superposition of the two waves?

A) y(x, t) = 7.4 cm sin(1000 rad/s t + 50.0 m⁻¹ x)
B) y(x, t) = 1.0 cm sin(1000 rad/s t − 50.0 m⁻¹ x)
C) y(x, t) = 1.0 cm sin(1000 rad/s t + 50.0 m⁻¹ x)
D) y(x, t) = 7.4 cm sin(1000 rad/s t − 50.0 m⁻¹ x)

Question 65

A length of piano wire is used to hang a mass from the ceiling. If the total mass of the string is 0.72 g and the mass hung from it is 1850 g, what is the length of the wire, assuming the fundamental frequency when plucked in these circumstances is 320 Hz?

A) 2.48 cm
B) 6.15 cm
C) 3.08 cm
D) 1.54 cm

Question 66

A microphone records sound produced from two speakers. As the microphone is moved around, a position at which the microphone receives a minimum intensity is found. If the intensity of one of the sound waves alone at that location is 0.055 W/m², and if the microphone receives an intensity of 0.004 W/m² there, what is a possible value for the intensity of the other source at the microphone's location?

A) Need more info to solve.
B) 0.089 W/m²
C) 0.051 W/m²
D) 0.048 W/m²

Question 67

Two speakers, facing each other, produce coherent sound waves that interfere destructively at a point that is ¾ of the way from one speaker to the other. If the speed of sound is 343 m/s, and the sound waves are emitted in phase at 880 Hz, which of the following is a possible distance between the two speakers?

A) 2.7 m
B) 0.58 m
C) 1.56 m
D) 2.3 m
E) 77 cm

Question 68

A longitudinal wave is represented by the equation z(z, t) = −2.0 cm sin(1,200 rad/s t − 20 m⁻¹ z). Another longitudinal wave is represented by the equation z(z, t) = +2.0 cm sin(1,200 rad/s t + 20 m⁻¹ z). What is the equation that represents the superposition of the two waves?

A) z(z, t) = -4.0 cm cos(1,200 rad/s t) sin(20 m−1 z)
B) z(z, t) = +4.0 cm cos(1,200 rad/s t) sin(20 m⁻¹ z)
C) z(z, t) = +4.0 cm cos(1,200 rad/s t) cos(20 m⁻¹ z)
D) z(z, t) = −2.0 cm cos(1,200 rad/s t) sin(20 m⁻¹ z)

Question 69

The speed of sound in air is dependent upon the air temperature and other factors. The speed of sound increases from 334 m/s to 341 m/s between 8:00am and 11:00am. If a horn produces sound with wavelength 0.75 m at 8:00am, what would it produce at 11:00am, assuming the frequency is unchanged?

A) 73 cm
B) 77 cm
C) Not enough info given to solve.
D) 75 cm

Question 70

Two guitar strings are under the same tension and have the same length. If their fundamental frequencies are in a ratio of 3:2, what is the ratio of their masses?

A) 3/2
B) 2/3
C) 9/4
D) 4/9

Question 71

What is the mass of a 1.25 m long piano wire that has a fundamental frequency of 256 Hz when under a tension of 552 N?

A) 6.4 g
B) 1.7 g
C) 3.4 g
D) 41 g
E) 4.1 g

Question 72

The following figure is a graph of a wave at a fixed position. The following figure is a graph of the same wave at a fixed time. What is the velocity of the wave in the above figure?

A) 150 m/s
B) 200 m/s
C) 250 m/s
D) 300 m/s
E) 450 m/s

Question 73

A guitar string is supposed to be played with a fundamental frequency of 880 Hz. If it is determined to have, instead, a fundamental frequency of 882 Hz, by what amount (as a percentage) must the tension in the string be changed in order that the fundamental frequency be restored to 880 Hz?

A) −0.45%
B) +0.45%
C) −0.11%
D) −0.23%

Question 74

What is the frequency of the wave?

A) 80 Hz
B) 50 Hz
C) 120 Hz
D) 140 Hz
E) 160 Hz

Question 75

A pair of speakers emits coherent sound waves in phase at a frequency of 440 Hz. A microphone is placed such that it is 1.0 m from one speaker on a line that is perpendicular to the line between the speakers. Which of the following distances reflects a possible distance between the speakers if there is complete destructive interference at the location of the microphone? The speed of sound is 340 m/s.

A) 1.0 m
B) 0.77 m
C) 2.76 m
D) 1.3 m
E) 1.77 m

Question 76

A transverse periodic wave is represented by the equation y(z, t) = −2.0 cm sin(1,200 rad/s t − 20.0 m⁻¹ x). Another transverse wave is represented by the equation y(z, t) = +2.0 cm sin(1,200 rad/s t + 20.0 m⁻¹ z). What is the equation that represents the superposition of the two waves?

A) y(z, t) = 4.0 cm sin(1,200 rad/s t − 20.0 m⁻¹ z)
B) y(x, t) = 4.0 cm sin(1,200 rad/s t) cos (20.0 m⁻¹ x)
C) y(x, t) = 4.0 cm cos(1,200 rad/s t) sin (20.0 m⁻¹ x)
D) y(x, t) = 4.0 cm cos(1,200 rad/s t + 20.0 m⁻¹ x)

Question 77

A wave is traveling with a velocity of 350 m/s and strikes a surface at an angle of 30.0 degrees with the normal to the surface. The wave splits into a reflected part and a refracted part. The refracted wave travels with a velocity of 300 m/s. What is the angle of refraction?

A) 50.4 degrees
B) 45.2 degrees
C) 40.4 degrees
D) 38.4 degrees
E) 25.4 degrees

Question 78

A wave is traveling with a velocity of 300 m/s and strikes a surface at an angle of 30.0 degrees with the normal to the surface. The wave splits into a reflected part and a refracted part. The refracted wave travels with a velocity of 400 m/s. What is the angle of refraction?

A) 20.5 degrees
B) 25.9 degrees
C) 30.5 degrees
D) 41.8 degrees
E) 50.3 degrees

Question 79

A guitar string has a tension of 95 N and is 75 cm long. If its mass is 0.27 g, what is the frequency of the first resonance above the fundamental?

A) 685 Hz
B) 69 Hz
C) 217 Hz
D) 470 kHz

Question 80

When light traveling in air passes into a sheet of glass, it is observed to change in wavelength to 58% of its wavelength in air. The speed of light in air is 3.0 × 10⁸ m/s. What is the speed of light in the glass?

A) 5.2 × 10⁸ m/s
B) 1.7 × 10⁸ m/s
C) 3.0 × 10⁸ m/s
D) 2.3 × 10⁸ m/s