Question 1

A wave is described by y(x,t)= 0.1 sin(3x + 10t), where x is in meters, y is in centimeters and t is in seconds.The angular wave number is:

Accepted Answer

A) 0.10 rad/m 
B) 3 $\pi$ rad/m 
C) 10 rad/m 
D) 10 $\pi$ rad/m 
E) 3.0 rad/m 
A) 0.10 rad/m 
B) 3 $\pi$ rad/m 
C) 10 rad/m 
D) 10 $\pi$ rad/m 
E) 3.0 rad/m

Question 2

The sum of two sinusoidal traveling waves is a sinusoidal traveling wave only if:

Accepted Answer

A) their amplitudes are the same and they travel in the same direction 
B) their amplitudes are the same and they travel in opposite directions 
C) their frequencies are the same and they travel in the same direction 
D) their frequencies are the same and they travel in opposite directions 
E) their frequencies are the same and their amplitudes are the same 
A) their amplitudes are the same and they travel in the same direction 
B) their amplitudes are the same and they travel in opposite directions 
C) their frequencies are the same and they travel in the same direction 
D) their frequencies are the same and they travel in opposite directions 
E) their frequencies are the same and their amplitudes are the same

Question 3

In the figure, a wave is traveling from left to right.If the point marked "D" represents the origin at time t = 0, and the displacement of the wave is given by y(x,t)= ymsin(kx -  $ \omega $t - $\phi$), what is the phase constant $\phi$

Accepted Answer

A) 0 
B) π/6 
C) π/4 
D) π/2 
E) 3π/2 
A) 0 
B) π/6 
C) π/4 
D) π/2 
E) 3π/2

Question 4

This plot shows the displacement of a string as a function of time, as a sinusoidal wave travels along it.Which letter corresponds to the amplitude of the wave?

Accepted Answer

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

Question 5

When a certain string is clamped at both ends, the lowest four resonant frequencies are 50, 100, 150, and 200 Hz.When the string is also clamped at its midpoint, the lowest four resonant frequencies are:

Accepted Answer

A) 50, 100, 150, and 200 Hz 
B) 50, 150, 250, and 300 Hz 
C) 100, 200, 300, and 400 Hz 
D) 25, 50 75, and 100 Hz 
E) 75, 150, 225, and 300 Hz 
A) 50, 100, 150, and 200 Hz 
B) 50, 150, 250, and 300 Hz 
C) 100, 200, 300, and 400 Hz 
D) 25, 50 75, and 100 Hz 
E) 75, 150, 225, and 300 Hz

Question 6

Two identical but separate strings, with the same tension, carry sinusoidal waves with the same amplitude.Wave A has a frequency that is twice that of wave B and transmits energy at a rate that is __________ that of wave B.

Accepted Answer

A) half 
B) twice 
C) one-fourth 
D) four times 
E) eight times 
A) half 
B) twice 
C) one-fourth 
D) four times 
E) eight times

Question 7

If $\lambda$ is the wavelength of the each of the component sinusoidal traveling waves that form a standing wave, the distance between adjacent nodes in the standing wave is:

Accepted Answer

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

Question 8

The displacement of a string is given by y(x,t)= ymsin(kx +  $ \omega $t).
The speed of the wave is:

Accepted Answer

A) "2 $\pi$k/ $ \omega $" 
B) " $ \omega $/k" 
C) " $ \omega $k" 
D) "2 $\pi$/k" 
E) "k/2 $\pi$" 
A) "2 $\pi$k/ $ \omega $" 
B) " $ \omega $/k" 
C) " $ \omega $k" 
D) "2 $\pi$/k" 
E) "k/2 $\pi$"

Question 9

A standing wave pattern is established in a string as shown.The wavelength of one of the component traveling waves is:

Accepted Answer

A) 0.25 m 
B) 0.5 m 
C) 1 m 
D) 2 m 
E) 4 m 
A) 0.25 m 
B) 0.5 m 
C) 1 m 
D) 2 m 
E) 4 m

Question 10

The displacement of a string carrying a traveling sinusoidal wave is given by   At time t = 0 the point at x = 0 has velocity v0 and displacement y0.The phase constant $\phi$is given by tan$\phi$=:

Accepted Answer

A) "v0/$ \omega $y0" 
B) "$ \omega $y0/v0" 
C) "$ \omega $v0/y0" 
D) "y0/$ \omega $v0" 
E) "$ \omega $v0y0" 
A) "v0/$ \omega $y0" 
B) "$ \omega $y0/v0" 
C) "$ \omega $v0/y0" 
D) "y0/$ \omega $v0" 
E) "$ \omega $v0y0"

Question 11

A long string is constructed by joining the ends of two shorter strings.The tension in the strings is the same but string I has 4 times the linear mass density of string II.When a sinusoidal wave passes from string I to string II:

Accepted Answer

A) the frequency decreases by a factor of 4 
B) the frequency decreases by a factor of 2 
C) the wavelength decreases by a factor of 4 
D) the wavelength decreases by a factor of 2 
E) the wavelength increases by a factor of 2 
A) the frequency decreases by a factor of 4 
B) the frequency decreases by a factor of 2 
C) the wavelength decreases by a factor of 4 
D) the wavelength decreases by a factor of 2 
E) the wavelength increases by a factor of 2

Question 12

Two waves are traveling on two different strings.The displacement of one is given by y1(x,t)= ymsin(kx + $ \omega $t)and of the other by y2(x,t)= ymsin(kx + $ \omega $t + φ).What is the difference between these two waves?

Accepted Answer

A) The displacement of wave y1 is always greater than the displacement of wave y2. 
B) Wave y1 has a smaller amplitude than wave y2. 
C) Wave y1 has a higher frequency than wave y2. 
D) Wave y1 has a shorter wavelength than wave y2. 
E) The two waves are identical except for their displacement at time t = 0. 
A) The displacement of wave y1 is always greater than the displacement of wave y2. 
B) Wave y1 has a smaller amplitude than wave y2. 
C) Wave y1 has a higher frequency than wave y2. 
D) Wave y1 has a shorter wavelength than wave y2. 
E) The two waves are identical except for their displacement at time t = 0.

Question 13

Let f be the frequency, v the speed, and T the period of a sinusoidal traveling wave.The correct relationship is:

Accepted Answer

A) f = 1/T 
B) f = v + T 
C) f = vT 
D) f = v/T 
E) f = T/v 
A) f = 1/T 
B) f = v + T 
C) f = vT 
D) f = v/T 
E) f = T/v

Question 14

A string carries a sinusoidal wave with an amplitude of 2.0 cm and a frequency of 100 Hz.The maximum speed of any point on the string is:

Accepted Answer

A) 2.0 m/s 
B) 4.0 m/s 
C) 6.3 m/s 
D) 13 m/s 
E) unknown (not enough information is given) 
A) 2.0 m/s 
B) 4.0 m/s 
C) 6.3 m/s 
D) 13 m/s 
E) unknown (not enough information is given)

Question 15

A sinusoidal transverse wave is traveling on a string.Any point on the string:

Accepted Answer

A) moves in the same direction as the wave 
B) moves in simple harmonic motion with a different frequency than that of the wave 
C) moves in simple harmonic motion with the same angular frequency as the wave 
D) moves in uniform circular motion with a different angular speed than the wave 
E) moves in uniform circular motion with the same angular speed as the wave 
A) moves in the same direction as the wave 
B) moves in simple harmonic motion with a different frequency than that of the wave 
C) moves in simple harmonic motion with the same angular frequency as the wave 
D) moves in uniform circular motion with a different angular speed than the wave 
E) moves in uniform circular motion with the same angular speed as the wave

Question 16

Sinusoidal waves travel on five identical strings.Four of the strings have the same tension, but the fifth has a different tension.Use the mathematical forms of the waves, gives below, to identify the string with the different tension.In the expressions given below x and y are in centimeters and t is in seconds.

Accepted Answer

A) y(x,t)= (2 cm)sin (2x - 4t) 
B) y(x,t)= (2 cm)sin (4x - 10t) 
C) y(x,t)= (2 cm)sin (6x - 12t) 
D) y(x,t)= (2 cm)sin (8x - 16t) 
E) y(x,t)= (2 cm)sin (10x - 20t) 
A) y(x,t)= (2 cm)sin (2x - 4t) 
B) y(x,t)= (2 cm)sin (4x - 10t) 
C) y(x,t)= (2 cm)sin (6x - 12t) 
D) y(x,t)= (2 cm)sin (8x - 16t) 
E) y(x,t)= (2 cm)sin (10x - 20t)

Question 17

The displacement of a string carrying a traveling sinusoidal wave is given by   At time t = 0 the point at x = 0 has a displacement of 0 and is moving in the positive y direction.The phase constant $\phi$is:

Accepted Answer

A) 0$\degree$ 
B) 90$\degree$ 
C) 135$\degree$ 
D) 180$\degree$ 
E) 270$\degree$ 
A) 0$\degree$ 
B) 90$\degree$ 
C) 135$\degree$ 
D) 180$\degree$ 
E) 270$\degree$

Question 18

A wave is described by y(x,t)= 0.1 sin(3x - 10t), where x is in meters, y is in centimeters and t is in seconds.How long does it take the wave to travel 2.0 m?

Accepted Answer

A) 0.6 s 
B) 1.0 s 
C) 3.0 s 
D) 6.7 s 
E) 10 s 
A) 0.6 s 
B) 1.0 s 
C) 3.0 s 
D) 6.7 s 
E) 10 s

Question 19

A standing wave:

Accepted Answer

A) can be constructed from two similar waves traveling in opposite directions 
B) must be transverse 
C) must be longitudinal 
D) has motionless points that are closer than half a wavelength 
E) has a wave velocity that differs by a factor of two from what it would be for a traveling wave 
A) can be constructed from two similar waves traveling in opposite directions 
B) must be transverse 
C) must be longitudinal 
D) has motionless points that are closer than half a wavelength 
E) has a wave velocity that differs by a factor of two from what it would be for a traveling wave

Question 20

The tension in a string with a linear density of 0.0010 kg/m is 0.40 N.A 100 Hz sinusoidal wave on this string has a wavelength of:

Accepted Answer

A) 0.20 cm 
B) 2.0 cm 
C) 5.0 cm 
D) 20 cm 
E) 400 cm 
A) 0.20 cm 
B) 2.0 cm 
C) 5.0 cm 
D) 20 cm 
E) 400 cm

Exam 16: Waves I

A wave is described by y(x,t)= 0.1 sin(3x + 10t), where x is in meters, y is in centimeters and t is in seconds.The angular wave number is:

The sum of two sinusoidal traveling waves is a sinusoidal traveling wave only if:

In the figure, a wave is traveling from left to right.If the point marked "D" represents the origin at time t = 0, and the displacement of the wave is given by y(x,t)= ymsin(kx - ω \omega ω t - ϕ\phiϕ ), what is the phase constant ϕ\phiϕ

This plot shows the displacement of a string as a function of time, as a sinusoidal wave travels along it.Which letter corresponds to the amplitude of the wave?

When a certain string is clamped at both ends, the lowest four resonant frequencies are 50, 100, 150, and 200 Hz.When the string is also clamped at its midpoint, the lowest four resonant frequencies are:

Two identical but separate strings, with the same tension, carry sinusoidal waves with the same amplitude.Wave A has a frequency that is twice that of wave B and transmits energy at a rate that is __________ that of wave B.

If λ\lambdaλ is the wavelength of the each of the component sinusoidal traveling waves that form a standing wave, the distance between adjacent nodes in the standing wave is:

The displacement of a string is given by y(x,t)= ymsin(kx + ω \omega ω t). The speed of the wave is:

A standing wave pattern is established in a string as shown.The wavelength of one of the component traveling waves is:

The displacement of a string carrying a traveling sinusoidal wave is given by At time t = 0 the point at x = 0 has velocity v0 and displacement y0.The phase constant ϕ\phiϕ is given by tan ϕ\phiϕ =:

A long string is constructed by joining the ends of two shorter strings.The tension in the strings is the same but string I has 4 times the linear mass density of string II.When a sinusoidal wave passes from string I to string II:

Two waves are traveling on two different strings.The displacement of one is given by y1(x,t)= ymsin(kx + ω \omega ω t)and of the other by y2(x,t)= ymsin(kx + ω \omega ω t + φ).What is the difference between these two waves?

Let f be the frequency, v the speed, and T the period of a sinusoidal traveling wave.The correct relationship is:

A string carries a sinusoidal wave with an amplitude of 2.0 cm and a frequency of 100 Hz.The maximum speed of any point on the string is:

A sinusoidal transverse wave is traveling on a string.Any point on the string:

The displacement of a string carrying a traveling sinusoidal wave is given by At time t = 0 the point at x = 0 has a displacement of 0 and is moving in the positive y direction.The phase constant ϕ\phiϕ is:

A wave is described by y(x,t)= 0.1 sin(3x - 10t), where x is in meters, y is in centimeters and t is in seconds.How long does it take the wave to travel 2.0 m?

A standing wave:

The tension in a string with a linear density of 0.0010 kg/m is 0.40 N.A 100 Hz sinusoidal wave on this string has a wavelength of:

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If $\lambda$ is the wavelength of the each of the component sinusoidal traveling waves that form a standing wave, the distance between adjacent nodes in the standing wave is:

The displacement of a string is given by y(x,t)= y_msin(kx + $\omega$ t). The speed of the wave is:

Two waves are traveling on two different strings.The displacement of one is given by y₁(x,t)= y_msin(kx + $\omega$ t)and of the other by y₂(x,t)= y_msin(kx + $\omega$ t + φ).What is the difference between these two waves?