Question 1

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

Accepted Answer

A)  1/T 
B)  2$\pi$/T 
C)  vT 
D)  f/T 
E)  T/f 
A)  1/T 
B)  2$\pi$/T 
C)  vT 
D)  f/T 
E)  T/f

Question 2

For a given medium, the frequency of a wave is:

Accepted Answer

A)  independent of wavelength 
B)  proportional to wavelength 
C)  inversely proportional to wavelength 
D)  proportional to the amplitude 
E)  inversely proportional to the amplitude 
A)  independent of wavelength 
B)  proportional to wavelength 
C)  inversely proportional to wavelength 
D)  proportional to the amplitude 
E)  inversely proportional to the amplitude

Question 3

The displacement of a string is given by   The wavelength of the wave is:

Accepted Answer

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

Question 4

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. At time t = 0, the point at x = 0 has a vertical displacement y = 0.0 cm. When is its displacement equal to 0.1 cm?

Accepted Answer

A)  0.16 s 
B)  0.47 s 
C)  2.5 s 
D)  7.5 s 
E)  10 s 
A)  0.16 s 
B)  0.47 s 
C)  2.5 s 
D)  7.5 s 
E)  10 s

Question 5

A sinusoidal wave is traveling toward the right as shown. Which letter correctly labels 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 6

Fully constructive interference between two sinusoidal waves of the same frequency occurs only if they:

Accepted Answer

A)  travel in the same direction and are 270 $\degree$ out of phase 
B)  travel in the same direction and are 45 $\degree$ out of phase 
C)  travel in the same direction and are in phase 
D)  travel in the same direction and are 180 $\degree$out of phase 
E)  travel in the same direction and are 90 $\degree$ out of phase 
A)  travel in the same direction and are 270 $\degree$ out of phase 
B)  travel in the same direction and are 45 $\degree$ out of phase 
C)  travel in the same direction and are in phase 
D)  travel in the same direction and are 180 $\degree$out of phase 
E)  travel in the same direction and are 90 $\degree$ out of phase

Question 7

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

Accepted Answer

A)  45$\degree$ 
B)  90$\degree$ 
C)  135$\degree$ 
D)  180$\degree$ 
E)  270$\degree$ 
A)  45$\degree$ 
B)  90$\degree$ 
C)  135$\degree$ 
D)  180$\degree$ 
E)  270$\degree$

Question 8

Two sinusoidal waves have the same angular frequency, the same amplitude ym, and travel in the same direction in the same medium. If they differ in phase by 50 $\degree$, the amplitude of the resultant wave is given by

Accepted Answer

A)  0.64 ym 
B)  1.3 ym 
C)  0.91 ym 
D)  1.8 ym 
E)  0.35 ym 
A)  0.64 ym 
B)  1.3 ym 
C)  0.91 ym 
D)  1.8 ym 
E)  0.35 ym

Question 9

When a 100-Hz oscillator is used to generate a sinusoidal wave on a certain string the wavelength is 10 cm. When the tension in the string is doubled the generator produces a wave with a frequency and wavelength of:

Accepted Answer

A)  200 Hz and 20 cm 
B)  141 Hz and 10 cm 
C)  100 Hz and 20 cm 
D)  100 Hz and 14 cm 
E)  50 Hz and 14 cm 
A)  200 Hz and 20 cm 
B)  141 Hz and 10 cm 
C)  100 Hz and 20 cm 
D)  100 Hz and 14 cm 
E)  50 Hz and 14 cm

Question 10

Two separated sources emit sinusoidal traveling waves that have the same wavelength $\lambda$ and are in phase at their respective sources. One travels a distance ℓ1 to get to the observation point while the other travels a distance ℓ2 The amplitude is a maximum at the observation point if ℓ1 − ℓ2 is:

Accepted Answer

A)  an odd multiple of  $\pi$/2 
B)  an odd multiple of $\lambda$/4 
C)  a multiple of $\lambda$ 
D)  an odd multiple of  $\pi$/2. 
E)  a multiple of  $\pi$ 
A)  an odd multiple of  $\pi$/2 
B)  an odd multiple of $\lambda$/4 
C)  a multiple of $\lambda$ 
D)  an odd multiple of  $\pi$/2. 
E)  a multiple of  $\pi$

Question 11

Suppose the maximum speed of a string carrying a sinusoidal wave is vs. When the displacement of a point on the string is half its maximum, the speed of the point is:

Accepted Answer

A)  vs/2 
B)  2vs 
C)  vs/4 
D)  3vs/4 
E)    
A)  vs/2 
B)  2vs 
C)  vs/4 
D)  3vs/4 
E)

Question 12

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 13

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 14

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 15

A sinusoidal wave is generated by moving the end of a string up and down periodically. The generator must supply the greatest power when the end of the string:

Accepted Answer

A)  has its greatest acceleration 
B)  has its greatest displacement 
C)  has half its greatest displacement 
D)  has one fourth its greatest displacement 
E)  has its least displacement 
A)  has its greatest acceleration 
B)  has its greatest displacement 
C)  has half its greatest displacement 
D)  has one fourth its greatest displacement 
E)  has its least displacement

Question 16

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 17

The time required for a small pulse to travel from A to B on a stretched cord shown is NOT altered by changing:

Accepted Answer

A)  the linear mass density of the cord 
B)  the length between A and B 
C)  the shape of the pulse 
D)  the tension in the cord 
E)  none of the above (changes in all alter the time) 
A)  the linear mass density of the cord 
B)  the length between A and B 
C)  the shape of the pulse 
D)  the tension in the cord 
E)  none of the above (changes in all alter the time)

Question 18

Two sinusoidal waves travel along the same string. They have the same wavelength and frequency. Their amplitudes are ym1 = 2.5 mm and ym2 = 4.5 mm, and their phases are π/4 rad and π/2 rad, respectively. What are the amplitude and phase of the resultant wave?

Accepted Answer

A)  cannot solve without knowing the wavelength 
B)  5.1 mm, 0.51 rad 
C)  5.1 mm, 0.79 rad 
D)  6.5 mm, 1.3 rad 
E)  7.0 mm, 1.3 rad 
A)  cannot solve without knowing the wavelength 
B)  5.1 mm, 0.51 rad 
C)  5.1 mm, 0.79 rad 
D)  6.5 mm, 1.3 rad 
E)  7.0 mm, 1.3 rad

Question 19

Two separated sources emit sinusoidal traveling waves that have the same wavelength $\lambda$ and are in phase at their respective sources. One travels a distance ℓ1 to get to the observation point while the other travels a distance ℓ2. The amplitude is a minimum at the observation point if ℓ1 − ℓ2 is:

Accepted Answer

A)  an odd multiple of $\lambda$/2 
B)  an odd multiple of $\lambda$/4 
C)  a multiple of$\lambda$ 
D)  an odd multiple of  $\pi$/2 
E)  a multiple of  $\pi$ 
A)  an odd multiple of $\lambda$/2 
B)  an odd multiple of $\lambda$/4 
C)  a multiple of$\lambda$ 
D)  an odd multiple of  $\pi$/2 
E)  a multiple of  $\pi$

Question 20

The transverse wave shown is traveling from left to right in a medium. The direction of the instantaneous velocity of the medium at point P is:

Accepted Answer

A)  $\uparrow$ 
B)  $\downarrow$ 
C)  $\rightarrow$ 
D)    
E)  no direction since v = 0 
A)  $\uparrow$ 
B)  $\downarrow$ 
C)  $\rightarrow$ 
D)    
E)  no direction since v = 0

Exam 16: Waves I

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

For a given medium, the frequency of a wave is:

The displacement of a string is given by The wavelength of the wave 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. At time t = 0, the point at x = 0 has a vertical displacement y = 0.0 cm. When is its displacement equal to 0.1 cm?

A sinusoidal wave is traveling toward the right as shown. Which letter correctly labels the amplitude of the wave?

Fully constructive interference between two sinusoidal waves of the same frequency occurs only if they:

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

Two sinusoidal waves have the same angular frequency, the same amplitude ym, and travel in the same direction in the same medium. If they differ in phase by 50 °\degree° , the amplitude of the resultant wave is given by

When a 100-Hz oscillator is used to generate a sinusoidal wave on a certain string the wavelength is 10 cm. When the tension in the string is doubled the generator produces a wave with a frequency and wavelength of:

Suppose the maximum speed of a string carrying a sinusoidal wave is vs. When the displacement of a point on the string is half its maximum, the speed of the point is:

A standing wave:

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:

A sinusoidal wave is generated by moving the end of a string up and down periodically. The generator must supply the greatest power when the end of the string:

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.

The time required for a small pulse to travel from A to B on a stretched cord shown is NOT altered by changing:

Two sinusoidal waves travel along the same string. They have the same wavelength and frequency. Their amplitudes are ym1 = 2.5 mm and ym2 = 4.5 mm, and their phases are π/4 rad and π/2 rad, respectively. What are the amplitude and phase of the resultant wave?

The transverse wave shown is traveling from left to right in a medium. The direction of the instantaneous velocity of the medium at point P is:

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Two sinusoidal waves have the same angular frequency, the same amplitude y_m, and travel in the same direction in the same medium. If they differ in phase by 50 $\degree$ , the amplitude of the resultant wave is given by

Suppose the maximum speed of a string carrying a sinusoidal wave is v_s. When the displacement of a point on the string is half its maximum, the speed of the point is:

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:

Two sinusoidal waves travel along the same string. They have the same wavelength and frequency. Their amplitudes are y_m1 = 2.5 mm and y_m2 = 4.5 mm, and their phases are π/4 rad and π/2 rad, respectively. What are the amplitude and phase of the resultant wave?