Deck 11: Waves

Question 1

intensity of the sound wave from an airplane is $1.0 \times 10^{2} \mathrm{~W} / \mathrm{m}^{2}$ at $5.0 \mathrm{~m}$ . What is the intensity at $100 \mathrm{~m}$ ?

A) $0.25 \mathrm{~mW} / \mathrm{m}^{2}$
B) $0.25 \mathrm{~W} / \mathrm{m}^{2}$
C) $0.53 \mathrm{~W} / \mathrm{m}^{2}$
D) $5.0 \mathrm{~W} / \mathrm{m}^{2}$

Answer 1

$0.25 \mathrm{~W} / \mathrm{m}^{2}$

Question 2

sound source of power 100 watts radiates sound uniformly in all directions. The intensity of the sound at a distance of $4.00 \mathrm{~m}$ is

A) $0.497 \mathrm{~W} / \mathrm{m}^{2}$ .
B) $0.301 \mathrm{~W} / \mathrm{m}^{2}$ .
C) $0.535 \mathrm{~W} / \mathrm{m}^{2}$ .
D) $0.353 \mathrm{~W} / \mathrm{m}^{2}$ .
E) $0.621 \mathrm{~W} / \mathrm{m}^{2}$ .

Answer 2

$0.497 \mathrm{~W} / \mathrm{m}^{2}$ .

Question 3

sound source of power 150 watts radiates sound uniformly in all directions. The intensity of the sound at a distance of $4.00 \mathrm{~m}$ is

A) $0.403 \mathrm{~W} / \mathrm{m}^{2}$ .
B) $0.389 \mathrm{~W} / \mathrm{m}^{2}$ .
C) $0.582 \mathrm{~W} / \mathrm{m}^{2}$ .
D) $0.746 \mathrm{~W} / \mathrm{m}^{2}$ .
E) $0.927 \mathrm{~W} / \mathrm{m}^{2}$ .

Answer 3

$0.746 \mathrm{~W} / \mathrm{m}^{2}$ .

Question 4

string with a length of $2.50 \mathrm{~m}$ has a mass of $5.00 \mathrm{~g}$ . The velocity of wave propagation along the string is $210 \mathrm{~m} / \mathrm{s}$ . The tension of the stretched string is

A) $66.7 \mathrm{~N}$ .
B) $70.2 \mathrm{~N}$ .
C) $88.2 \mathrm{~N}$ .
D) $75.0 \mathrm{~N}$ .
E) $60.2 \mathrm{~N}$ .

Question 5

string on a violin is stretched between two points $20.00 \mathrm{~cm}$ apart with a tension of $120.0 \mathrm{~N}$ . The mass/length of the string is $0.002000 \mathrm{~kg} / \mathrm{m}$ . The frequency of the $2^{\text {nd }}$ overtone is

A) $1,837 \mathrm{~Hz}$ .
B) $1,502 \mathrm{~Hz}$ .
C) $2,237 \mathrm{~Hz}$ .
D) $2,568 \mathrm{~Hz}$ .
E) $3,250 \mathrm{~Hz}$ .

Question 6

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

A) $1.33 \times 1014 \mathrm{~Hz}$ to $2.33 \times 1014 \mathrm{~Hz}$
B) $4.29 \times 1012 \mathrm{~Hz}$ to $7.50 \times 1012 \mathrm{~Hz}$
C) $1.33 \times 1012 \mathrm{~Hz}$ to $2.33 \times 10^{12} \mathrm{~Hz}$
D) $4.29 \times 10^{14} \mathrm{~Hz}$ to $7.50 \times 10^{14} \mathrm{~Hz}$

Question 7

transverse wave travels at $230.0 \mathrm{~m} / \mathrm{s}$ along the $y$ -axis. If the frequency of the periodic vibrations of the wave is $390.0 \mathrm{~Hz}$ , then what is the wavelength of the wave?

A) $58.97 \mathrm{~cm}$
B) $36.76 \mathrm{~cm}$
C) $40.89 \mathrm{~cm}$
D) $68.97 \mathrm{~cm}$
E) $47.23 \mathrm{~cm}$

Question 8

frequency of a periodic wave is $340 \mathrm{~Hz}$ . The period of the vibration motion of the wave is

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

Question 9

wavelength of a periodic wave is $0.750 \mathrm{~m}$ . If the frequency is $425 \mathrm{~Hz}$ , then what is the angular frequency $\omega$ of the wave?

A) $5.44 \times 10^{3} \mathrm{rad} / \mathrm{s}$
B) $4.21 \times 10^{3} \mathrm{rad} / \mathrm{s}$
C) $3.76 \times 10^{3} \mathrm{rad} / \mathrm{s}$
D) $5.03 \times 103 \mathrm{rad} / \mathrm{s}$
E) $2.67 \times 10^{3} \mathrm{rad} / \mathrm{s}$

Question 10

wavelength of a periodic wave is $0.800 \mathrm{~m}$ . If the frequency is $400 \mathrm{~Hz}$ , then what is the wavenumber $k$ of the wave?

A) $5.98 \mathrm{~m}^{-1}$
B) $8.56 \mathrm{~m}^{-1}$
C) $7.85 \mathrm{~m}^{-1}$
D) $6.35 \mathrm{~m}^{-1}$
E) $7.02 \mathrm{~m}^{-1}$

Question 11

wavelength of a periodic wave is $0.750 \mathrm{~m}$ . If the frequency is $365 \mathrm{~Hz}$ , then what is the angular frequency $\omega$ of the wave?

A) $3.10 \times 10^{3} \mathrm{rad} / \mathrm{s}$
B) $2.98 \times 10^{3} \mathrm{rad} / \mathrm{s}$
C) $3.87 \times 10^{3} \mathrm{rad} / \mathrm{s}$
D) $2.29 \times 10^{3} \mathrm{rad} / \mathrm{s}$
E) $1.75 \times 10^{3} \mathrm{rad} / \mathrm{s}$

Question 12

wavelength of a periodic wave is $0.500 \mathrm{~m}$ . If the frequency is $400 \mathrm{~Hz}$ , then what is the wavenumber $k$ of the wave?

A) $21.0 \mathrm{~m}^{-1}$
B) $25.9 \mathrm{~m}^{-1}$
C) $12.6 \mathrm{~m}^{-1}$
D) $18.4 \mathrm{~m}^{-1}$
E) $14.8 \mathrm{~m}^{-1}$

Question 13

longitudinal wave travels on a slinky or any long spring. The wave is represented by the equation $\mathrm{x}(\mathrm{x}, \mathrm{t})=2.1 \mathrm{~cm} \cos \left(2000 \mathrm{rad} / \mathrm{s} \mathrm{t}-40 \mathrm{~m}^{-1} \mathrm{x}\right)$ . What is the direction of propagation of the wave?

A) the $-y$ direction
B) the $-x$ direction
C) the $+x$ direction
D) the $+\mathrm{y}$ direction

Question 14

longitudinal wave travels on a slinky or any long spring. The wave is represented by the equation $\mathrm{x}(\mathrm{x}, \mathrm{t})=2.1 \mathrm{~cm} \cos \left(2000 \mathrm{rad} / \mathrm{s} \mathrm{t}-40 \mathrm{~m}^{-1} \mathrm{x}\right)$ . What is the direction of motion of a point on the spring due to the wave?

A) the $\pm \mathrm{z}$ direction
B) the $\pm \mathrm{x}$ direction
C) the \textbackslash pm y direction

Question 15

longitudinal wave travels on a slinky or any long spring. The wave is represented by the equation $\mathrm{x}(\mathrm{x}, \mathrm{t})=$ $2.10 \mathrm{~cm} \cos \left(2000 \mathrm{rad} / \mathrm{s} t+40.0 \mathrm{~m}^{-1} \mathrm{x}\right)$ . What is the velocity of the wave?

A) $0.02 \mathrm{~m} / \mathrm{s}$ in the $+x$ direction
B) $50 \mathrm{~m} / \mathrm{s}$ in the $-x$ direction
C) $0.02 \mathrm{~m} / \mathrm{s}$ in the $-x$ direction
D) $50 \mathrm{~m} / \mathrm{s}$ in the $+x$ direction

Question 16

longitudinal wave travels on a slinky or any long spring. The wave is represented by the equation $\mathrm{z}(\mathrm{z}, \mathrm{t})=$ $1.2 \mathrm{~cm} \cos \left(1800 \mathrm{rad} / \mathrm{s} t+60 \mathrm{~m}^{-1} \mathrm{z}\right)$ . What are the wavenumber and direction of propagation of the wave?

A) $60 \mathrm{~m}^{-1}$ ; traveling in the $+\mathrm{z}$ direction
B) $60 \mathrm{~m}^{-1}$ ; traveling in the $-\mathrm{z}$ direction
C) $60 \mathrm{~m}^{-1}$ ; traveling in the $-x$ direction
D) $60 \mathrm{~m}^{-1}$ ; traveling in the $+x$ direction

Question 17

transverse periodic wave is represented by the equation $\mathrm{y}(\mathrm{x}, \mathrm{t})=2.50 \mathrm{~cm} \cos \left(2,500 \mathrm{rad} / \mathrm{st}-15.0 \mathrm{~m}^{-1} \mathrm{x}\right)$ . What is the direction of the vibration of the wave?

A) the $\mathrm{x}$ direction
B) the $\mathrm{z}$ direction
C) the $y$ direction

Question 18

transverse periodic wave is represented by the equation $y(x, t)=2.50 \mathrm{~cm} \cos \left(2,500 \mathrm{rad} / \mathrm{st}-15.0 \mathrm{~m}^{-1} \mathrm{x}\right)$ . What is the direction of the velocity of the wave?

A) the $-\mathrm{z}$ direction
B) the $-x$ direction
C) the $+x$ direction
D) the $-y$ direction
E) the $+y$ direction
F) the $+\mathrm{z}$ direction

Question 19

transverse periodic wave is represented by the equation $y(x, t)=2.50 \mathrm{~cm} \cos \left(2,500 \mathrm{rad} / \mathrm{s} t-15.0 \mathrm{~m}^{-1} \mathrm{x}\right)$ . What is the velocity of the wave?

A) $167 \mathrm{~m} / \mathrm{s}$ in the $-\mathrm{x}$ direction
B) $450 \mathrm{~m} / \mathrm{s}$ in the $-y$ direction
C) $333 \mathrm{~m} / \mathrm{s}$ in the $+\mathrm{y}$ direction
D) $333 \mathrm{~m} / \mathrm{s}$ in the $+x$ direction
E) $167 \mathrm{~m} / \mathrm{s}$ in the $+x$ direction

Question 20

transverse periodic wave is represented by the equation $y(x, t)=2.50 \mathrm{~cm} \cos \left(2,500 \mathrm{rad} / \mathrm{s} t-15.0 \mathrm{~m}^{-1} \mathrm{x}\right)$ . What are the wavenumber $k$ and direction of propagation of the wave?

A) $15.0 \mathrm{~m}^{-1}$ ; traveling in the $+\mathrm{x}$ direction
B) $30.0 \mathrm{~m}^{-1}$ ; traveling in the $+\mathrm{y}$ direction
C) $15.0 \mathrm{~m}^{-1}$ ; traveling in the $-\mathrm{x}$ direction
D) $45.0 \mathrm{~m}^{-1}$ ; traveling in the $+x$ direction
E) $30.0 \mathrm{~m}^{-1}$ ; traveling in the $-\mathrm{y}$ direction

Question 21

transverse periodic wave is represented by the equation $y(x, t)=2.50 \mathrm{~cm} \cos \left(2,500 \mathrm{rad} / \mathrm{st}-15.0 \mathrm{~m}^{-1} \mathrm{x}\right)$ . What is the frequency of the vibration of the wave?

A) $398 \mathrm{~Hz}$
B) $422 \mathrm{~Hz}$
C) $302 \mathrm{~Hz}$
D) $490 \mathrm{~Hz}$
E) $467 \mathrm{~Hz}$

Question 22

transverse periodic wave is represented by the equation $\mathrm{z}(\mathrm{y}, \mathrm{t})=1.50 \mathrm{~cm} \sin \left(1,250 \mathrm{rad} / \mathrm{s} \mathrm{t}+10.0 \mathrm{~m}^{-1} \mathrm{y}\right)$ . What is the direction of the vibration of the wave?

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

Question 23

transverse periodic wave is represented by the equation $\mathrm{z}(\mathrm{y}, \mathrm{t})=1.50 \mathrm{~cm} \sin \left(1,250 \mathrm{rad} / \mathrm{s} \mathrm{t}+10.0 \mathrm{~m}^{-1} \mathrm{y}\right)$ . What is the direction of the velocity of the wave?

A) the $\mathrm{z}$ direction
B) the y direction
C) the $\mathrm{t}$ direction
D) the $\mathrm{x}$ direction

Question 24

transverse periodic wave is represented by the equation $\mathrm{z}(\mathrm{y}, \mathrm{t})=1.50 \mathrm{~cm} \sin \left(1,250 \mathrm{rad} / \mathrm{s} \mathrm{t}+10.0 \mathrm{~m}^{-1} \mathrm{y}\right)$ . What is the velocity of the wave?

A) $125 \mathrm{~m} / \mathrm{s}$ in the $-\mathrm{y}$ direction
B) $250 \mathrm{~m} / \mathrm{s}$ in the $-\mathrm{z}$ direction
C) $125 \mathrm{~m} / \mathrm{s}$ in the $+\mathrm{z}$ direction
D) $250 \mathrm{~m} / \mathrm{s}$ in the $-\mathrm{y}$ direction
E) $125 \mathrm{~m} / \mathrm{s}$ in the $+\mathrm{y}$ direction

Question 25

transverse periodic wave is represented by the equation $\mathrm{z}(\mathrm{y}, \mathrm{t})=1.50 \mathrm{~cm} \sin \left(1,250 \mathrm{rad} / \mathrm{st}+10.0 \mathrm{~m}^{-1} \mathrm{y}\right)$ . What are the wavenumber $k$ and direction of propagation of the wave?

A) $20 \mathrm{~m}^{-1}$ ; traveling in the $+\mathrm{z}$ direction
B) $10 \mathrm{~m}^{-1}$ ; traveling in the $-\mathrm{y}$ direction
C) $10 \mathrm{~m}^{-1}$ ; traveling in the $+\mathrm{y}$ direction
D) $20 \mathrm{~m}^{-1}$ ; traveling in the $-\mathrm{z}$ direction
E) $10 \mathrm{~m}^{-1}$ ; traveling in the $-\mathrm{z}$ direction

Question 26

transverse periodic wave is represented by the equation $\mathrm{z}(\mathrm{y}, \mathrm{t})=1.50 \mathrm{~cm} \sin \left(1,250 \mathrm{rad} / \mathrm{s} t+10.0 \mathrm{~m}^{-1} \mathrm{y}\right)$ . What is the frequency of the vibration of the wave?

A) $240 \mathrm{~Hz}$
B) $199 \mathrm{~Hz}$
C) $289 \mathrm{~Hz}$
D) $319 \mathrm{~Hz}$
E) $150 \mathrm{~Hz}$

Question 27

transverse periodic wave is represented by the equation $\mathrm{y}(\mathrm{x}, \mathrm{t})=1.50 \mathrm{~cm} \sin \left(1,500 \mathrm{rad} / \mathrm{s} \mathrm{t}-10.0 \mathrm{~m}^{-1} \mathrm{x}\right)$ . Another transverse wave is represented by the equation $y(x, t)=1.50 \mathrm{~cm} \sin \left(1,500 \mathrm{rad} / \mathrm{s} t-10.0 \mathrm{~m}^{-1} \mathrm{x}\right)$ . What is the equation that represents the superposition of the two waves?

A) $\mathrm{y}(\mathrm{x}, \mathrm{t})=3.0 \mathrm{~cm} \sin \left(1,500 \mathrm{rad} / \mathrm{st}+10.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
B) $y(x, t)=3.0 \mathrm{~cm} \sin \left(1,500 \mathrm{rad} / \mathrm{s}-10.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
C) $y(x, t)=3.0 \mathrm{~cm} \cos (1,500 \mathrm{rad} / \mathrm{s} t) \sin \left(10.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
D) $y(x, t)=3.0 \mathrm{~cm} \sin (1,500 \mathrm{rad} / \mathrm{st}) \cos \left(10.0 \mathrm{~m}^{-1} \mathrm{x}\right)$

Question 28

transverse periodic wave is represented by the equation $y(x, t)=1.50 \mathrm{~cm} \sin \left(1,500 \mathrm{rad} / \mathrm{s} t-10.0 \mathrm{~m}^{-1} \mathrm{x}\right)$ . Another transverse wave is represented by the equation $\mathrm{y}(\mathrm{x}, \mathrm{t})=1.50 \mathrm{~cm} \sin \left(1,500 \mathrm{rad} / \mathrm{s} \mathrm{t}+10.0 \mathrm{~m}^{-1} \mathrm{x}\right)$ . What is the equation that represents the superposition of the two waves?

A) $y(x, t)=3.0 \mathrm{~cm} \cos (1,500 \mathrm{rad} / \mathrm{s} t) \sin \left(10.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
B) $y(x, t)=3.0 \mathrm{~cm} \sin (1,500 \mathrm{rad} / \mathrm{s} \mathrm{t}) \cos \left(10.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
C) $y(x, t)=3.0 \mathrm{~cm} \sin \left(1,500 \mathrm{rad} / \mathrm{s} t-10.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
D) $y(x, t)=3.0 \mathrm{~cm} \sin \left(1,500 \mathrm{rad} / \mathrm{st}+10.0 \mathrm{~m}^{-1} \mathrm{x}\right)$

Question 29

transverse periodic wave is represented by the equation $y(x, t)=-1.50 \mathrm{~cm} \sin \left(1,500 \mathrm{rad} / \mathrm{s} t-10.0 \mathrm{~m}^{-1}\right.$ $\mathrm{x})$ . Another transverse wave is represented by the equation $\mathrm{y}(\mathrm{x}, \mathrm{t})=+1.50 \mathrm{~cm} \sin \left(1,500 \mathrm{rad} / \mathrm{s} \mathrm{t}+10.0 \mathrm{~m}^{-1}\right.$ $\mathrm{x})$ . What is the equation that represents the superposition of the two waves?

A) $y(x, t)=3.0 \mathrm{~cm} \cos (1,500 \mathrm{rad} / \mathrm{st}) \sin \left(10.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
B) $y(x, t)=3.0 \mathrm{~cm} \sin \left(1,500 \mathrm{rad} / \mathrm{s} t-10.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
C) $y(x, t)=3.0 \mathrm{~cm} \sin (1,500 \mathrm{rad} / \mathrm{s} \mathrm{t}) \cos \left(10.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
D) $y(x, t)=3.0 \mathrm{~cm} \sin \left(1,500 \mathrm{rad} / \mathrm{s} t+10.0 \mathrm{~m}^{-1} \mathrm{x}\right)$

Question 30

transverse periodic wave is represented by the equation $\mathrm{y}(\mathrm{z}, \mathrm{t})=2.0 \mathrm{~cm} \sin \left(1,200 \mathrm{rad} / \mathrm{s} \mathrm{t}-20.0 \mathrm{~m}^{-1} \mathrm{z}\right)$ . Another transverse wave is represented by the equation $\mathrm{y}(\mathrm{z}, \mathrm{t})=2.0 \mathrm{~cm} \sin \left(1,200 \mathrm{rad} / \mathrm{s} \mathrm{t}-20.0 \mathrm{~m}^{-1} \mathrm{z}\right)$ . What is the equation that represents the superposition of the two waves?

A) $y(x, t)=4.0 \mathrm{~cm} \sin (1,200 \mathrm{rad} / \mathrm{st}) \cos \left(20.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
B) $\mathrm{y}(\mathrm{x}, \mathrm{t})=4.0 \mathrm{~cm} \cos \left(1,200 \mathrm{rad} / \mathrm{s} \mathrm{t}+20.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
C) $y(x, t)=4.0 \mathrm{~cm} \cos (1,200 \mathrm{rad} / \mathrm{s} t) \sin \left(20.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
D) $\mathrm{y}(\mathrm{z}, \mathrm{t})=4.0 \mathrm{~cm} \sin \left(1,200 \mathrm{rad} / \mathrm{s} \mathrm{t}-20.0 \mathrm{~m}^{-1} \mathrm{z}\right)$

Question 31

transverse periodic wave is represented by the equation $y(z, t)=2.0 \mathrm{~cm} \sin \left(1,200 \mathrm{rad} / \mathrm{s} t-20.0 \mathrm{~m}^{-1} \mathrm{z}\right)$ . Another transverse wave is represented by the equation $\mathrm{y}(\mathrm{z}, \mathrm{t})=2.0 \mathrm{~cm} \sin \left(1,200 \mathrm{rad} / \mathrm{s} \mathrm{t}+20.0 \mathrm{~m}^{-1} \mathrm{z}\right)$ . What is the equation that represents the superposition of the two waves?

A) $y(x, t)=4.0 \mathrm{~cm} \cos \left(1,200 \mathrm{rad} / \mathrm{s} \mathrm{t}+20.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
B) $y(x, t)=4.0 \mathrm{~cm} \sin (1,200 \mathrm{rad} / \mathrm{s} \mathrm{t}) \cos \left(20.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
C) $y(z, t)=4.0 \mathrm{~cm} \sin \left(1,200 \mathrm{rad} / \mathrm{s} \mathrm{t}-20.0 \mathrm{~m}^{-1} \mathrm{z}\right)$
D) $y(x, t)=4.0 \mathrm{~cm} \cos (1,200 \mathrm{rad} / \mathrm{s} t) \sin \left(20.0 \mathrm{~m}^{-1} \mathrm{x}\right)$

Question 32

transverse periodic wave is represented by the equation $y(z, t)=-2.0 \mathrm{~cm} \sin \left(1,200 \mathrm{rad} / \mathrm{s} t-20.0 \mathrm{~m}^{-1} \mathrm{x}\right)$ . Another transverse wave is represented by the equation $y(z, t)=+2.0 \mathrm{~cm} \sin \left(1,200 \mathrm{rad} / \mathrm{s} t+20.0 \mathrm{~m}^{-1} \mathrm{z}\right)$ . What is the equation that represents the superposition of the two waves?

A) $\mathrm{y}(\mathrm{z}, \mathrm{t})=4.0 \mathrm{~cm} \sin \left(1,200 \mathrm{rad} / \mathrm{s} \mathrm{t}-20.0 \mathrm{~m}^{-1} \mathrm{z}\right)$
B) $y(x, t)=4.0 \mathrm{~cm} \cos (1,200 \mathrm{rad} / \mathrm{s} t) \sin \left(20.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
C) $y(x, t)=4.0 \mathrm{~cm} \cos \left(1,200 \mathrm{rad} / \mathrm{s} t+20.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
D) $y(x, t)=4.0 \mathrm{~cm} \sin (1,200 \mathrm{rad} / \mathrm{st}) \cos \left(20.0 \mathrm{~m}^{-1} \mathrm{x}\right)$

Question 33

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.

A) $450 \mathrm{~m} / \mathrm{s}$
B) $150 \mathrm{~m} / \mathrm{s}$
C) $250 \mathrm{~m} / \mathrm{s}$
D) $200 \mathrm{~m} / \mathrm{s}$
E) $300 \mathrm{~m} / \mathrm{s}$

Question 34

wave is represented by the equation $y(x, t)=3.2 \mathrm{~cm} \sin \left(1000 \mathrm{rad} / \mathrm{s} t-50 \mathrm{~m}^{-1} \mathrm{x}\right)$ . Another wave, with the same wavelength and frequency, has an amplitude of $4.2 \mathrm{~cm}$ . If the two waves interfere constructively, then which equation could represent the superposition of the two waves?

A) $y(x, t)=7.4 \mathrm{~cm} \mathrm{sin}\left(1000 \mathrm{rad} / \mathrm{st}+50.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
B) $y(x, t)=1.0 \mathrm{~cm} \sin \left(1000 \mathrm{rad} / \mathrm{s} t+50.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
C) $y(x, t)=1.0 \mathrm{~cm} \sin \left(1000 \mathrm{rad} / \mathrm{s} \mathrm{t}-50.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
D) $y(x, t)=7.4 \mathrm{~cm} \sin \left(1000 \mathrm{rad} / \mathrm{s} \mathrm{t}-50.0 \mathrm{~m}^{-1} \mathrm{x}\right)$

Question 35

wave is represented by the equation $\mathrm{y}(\mathrm{x}, \mathrm{t})=3.2 \mathrm{~cm} \sin \left(1000 \mathrm{rad} / \mathrm{s} \mathrm{t}-50 \mathrm{~m}^{-1} \mathrm{x}\right)$ . Another wave, with the same wavelength and frequency, has an amplitude of $4.2 \mathrm{~cm}$ . If the two waves interfere destructively, then which equation could represent the superposition of the two waves?

A) $y(x, t)=7.4 \mathrm{~cm} \mathrm{sin}\left(1000 \mathrm{rad} / \mathrm{s} t-50.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
B) $y(x, t)=1.0 \mathrm{~cm} \sin \left(1000 \mathrm{rad} / \mathrm{s} t+50.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
C) $y(x, t)=7.4 \mathrm{~cm} \sin \left(1000 \mathrm{rad} / \mathrm{s} t+50.0 \mathrm{~m}^{-1} \mathrm{x}\right)$
D) $y(x, t)=1.0 \mathrm{~cm} \sin \left(1000 \mathrm{rad} / \mathrm{s} \mathrm{t}-50.0 \mathrm{~m}^{-1} \mathrm{x}\right)$

Question 36

longitudinal wave is represented by the equation $\mathrm{z}(\mathrm{z}, \mathrm{t})=-2.0 \mathrm{~cm} \sin \left(1,200 \mathrm{rad} / \mathrm{s} \mathrm{t}-20 \mathrm{~m}^{-1} \mathrm{z}\right)$ . Another longitudinal wave is represented by the equation $\mathrm{z}(\mathrm{z}, \mathrm{t})=+2.0 \mathrm{~cm} \sin \left(1,200 \mathrm{rad} / \mathrm{s} \mathrm{t}+20 \mathrm{~m}^{-1} \mathrm{z}\right)$ . What is the equation that represents the superposition of the two waves?

A) $\mathrm{z}(\mathrm{z}, \mathrm{t})=+4.0 \mathrm{~cm} \cos (1,200 \mathrm{rad} / \mathrm{s} \mathrm{t}) \cos \left(20 \mathrm{~m}^{-1} \mathrm{z}\right)$
B) $\mathrm{z}(\mathrm{z}, \mathrm{t})=+4.0 \mathrm{~cm} \cos (1,200 \mathrm{rad} / \mathrm{s} \mathrm{t}) \sin \left(20 \mathrm{~m}^{-1} \mathrm{z}\right)$
C) $\mathrm{z}(\mathrm{z}, \mathrm{t})=-2.0 \mathrm{~cm} \cos (1,200 \mathrm{rad} / \mathrm{s} \mathrm{t}) \sin \left(20 \mathrm{~m}^{-1} \mathrm{z}\right)$
D) $\mathrm{z}(\mathrm{z}, \mathrm{t})=-4.0 \mathrm{~cm} \cos (1,200 \mathrm{rad} / \mathrm{s} \mathrm{t}) \sin (20 \mathrm{~m}-1 \mathrm{z})$

Question 37

speakers are emitting coherent sound waves at a frequency of $440 \mathrm{~Hz}$ . The waves are emitted in phase. If the speed of sound is $343 \mathrm{~m} / \mathrm{s}$ , and it is observed that no sound is heard $17.2 \mathrm{~m}$ from one speaker, which of the following is a possible distance to the second speaker?

A) $14.5 \mathrm{~m}$
B) $18.0 \mathrm{~m}$
C) $18.8 \mathrm{~m}$
D) $17.2 \mathrm{~m}$
E) $19.6 \mathrm{~m}$
F) $16.5 \mathrm{~m}$

Question 38

cello plays a note of frequency $220 \mathrm{~Hz}$ using a length $L$ of one of its strings. What length of the same string must be used in order to play a fundamental frequency of $256 \mathrm{~Hz}$ ? Assume in each case that the note played is the fundamental frequency of the string at the given length and that the tension $\mathrm{T}$ and mass per unit length are not changed when selecting a different length of the same string.

A) $1.72 \mathrm{~L}$
B) $0.86 \mathrm{~L}$
C) $0.43 \mathrm{~L}$
D) $0.58 \mathrm{~L}$
E) $2.32 \mathrm{~L}$
F) $1.16 \mathrm{~L}$

Question 39

is the mass of a string that is $17 \mathrm{~cm}$ long and has a fundamental frequency of $792 \mathrm{~Hz}$ when under a tension of $1.7 \mathrm{kN}$ ?

A) $6.4 \mathrm{~g}$
B) $3.2 \mathrm{~g}$
C) $4.0 \mathrm{~g}$
D) $64 \mathrm{~g}$
E) $1.6 \mathrm{~g}$
F) $32 \mathrm{~g}$

Question 40

sound wave radiates from a source uniformly in all directions. If the power of the sound source is 200 watts, then the intensity of the sound wave $100 \mathrm{~m}$ from the source is

A) $2.2 \mathrm{~mW} / \mathrm{m}^{2}$
B) $1.2 \mathrm{~mW} / \mathrm{m}^{2}$ .
C) $1.8 \mathrm{~mW} / \mathrm{m}^{2}$ .
D) $1.6 \mathrm{~mW} / \mathrm{m}^{2}$ .
E) $2.0 \mathrm{~mW} / \mathrm{m}^{2}$ .

Question 41

speed of sound in water is 4.3 times the speed of sound in air. A whistle produces a sound wave in air with a frequency $\mathrm{f}_{0}$ . When this sound wave enters the water, its frequency will be

A) $\mathrm{f}_{0} / 4.3$ .
B) $4.3 \mathrm{f}_{0}$ .
C) $\mathrm{f}_{0}$ .
D) not enough information