Question 1

Here are equations for three waves traveling on separate strings.Rank them according to the maximum transverse speed, least to greatest.

Accepted Answer

A) 1, 2, 3 
B) 1, 3, 2 
C) 2, 1, 3 
D) 2, 3, 1 
E) 3, 1, 2 
A) 1, 2, 3 
B) 1, 3, 2 
C) 2, 1, 3 
D) 2, 3, 1 
E) 3, 1, 2

Question 2

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 3

A string of length 100 cm is held fixed at both ends and vibrates in a standing wave pattern.The wavelengths of the constituent traveling waves CANNOT be:

Accepted Answer

A) 400 cm 
B) 200 cm 
C) 100 cm 
D) 67 cm 
E) 50 cm 
A) 400 cm 
B) 200 cm 
C) 100 cm 
D) 67 cm 
E) 50 cm

Question 4

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 5

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

Accepted Answer

A) "2$\pi$k/   0" 
B) "F1F1F1S  /k" 
C) "   k" 
D) "2$\pi$/k" 
E) "k/2$\pi$" 
A) "2$\pi$k/   0" 
B) "F1F1F1S  /k" 
C) "   k" 
D) "2$\pi$/k" 
E) "k/2$\pi$"

Question 6

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    is:

Accepted Answer

A) 0° 
B) 90° 
C) 135° 
D) 180° 
E) 270° 
A) 0° 
B) 90° 
C) 135° 
D) 180° 
E) 270°

Question 7

Two sources, S1 and S2, each emit waves of wavelength  $\lambda$  in the same medium.The phase difference between the two waves, at the point P shown, is   .The quantity$\pi$ is:

Accepted Answer

A) "the distance S1S2" 
B) "the angle S1PS2" 
C) "$\pi$/2" 
D) "the phase difference between the two sources" 
E) "zero for transverse waves,  $\lambda$  for longitudinal waves" 
A) "the distance S1S2" 
B) "the angle S1PS2" 
C) "$\pi$/2" 
D) "the phase difference between the two sources" 
E) "zero for transverse waves,  $\lambda$  for longitudinal waves"

Question 8

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 frequency is:

Accepted Answer

A) 0.10 rad/s 
B) 3.0 rad/s 
C) 10$\pi$ rad/s 
D) 20$\pi$ rad/s 
E) 10 rad/s 
A) 0.10 rad/s 
B) 3.0 rad/s 
C) 10$\pi$ rad/s 
D) 20$\pi$ rad/s 
E) 10 rad/s

Question 9

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 10

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

Question 11

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 12

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 13

Two traveling sinusoidal waves interfere to produce a wave with the mathematical form   If the value of    is appropriately chosen, the two waves might be:

Accepted Answer

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

Question 14

The displacement of an element of a string is given by y(x,t)= 4. , with x in meters and t in seconds.Given that   , what is v?

Accepted Answer

A) 0.065 m/s 
B) 0.25 m/s 
C) 2.0 m/s 
D) 3.9 m/s 
E) 15 m/s 
A) 0.065 m/s 
B) 0.25 m/s 
C) 2.0 m/s 
D) 3.9 m/s 
E) 15 m/s

Question 15

A string, clamped at its ends, vibrates in three segments.The string is 100 cm long.The wavelength is:

Accepted Answer

A) 33 cm 
B) 67 cm 
C) 150 cm 
D) 300 cm 
E) need to know the frequency 
A) 33 cm 
B) 67 cm 
C) 150 cm 
D) 300 cm 
E) need to know the frequency

Question 16

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

Question 17

For a transverse wave on a string the string displacement is described by y(x,t)= f(x-at)where f is a given function and a is a positive constant.Which of the following does NOT necessarily follow from this statement?

Accepted Answer

A) The shape of the string at time t = 0 is given by f(x). 
B) The shape of the waveform does not change as it moves along the string. 
C) The waveform moves in the positive x direction. 
D) The speed of the waveform is a. 
E) The speed of the waveform is x/t. 
A) The shape of the string at time t = 0 is given by f(x). 
B) The shape of the waveform does not change as it moves along the string. 
C) The waveform moves in the positive x direction. 
D) The speed of the waveform is a. 
E) The speed of the waveform is x/t.

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 30-cm long string, with one end clamped and the other free to move transversely, is vibrating in its second harmonic.The wavelength of the constituent traveling waves is:

Accepted Answer

A) 10 cm 
B) 30 cm 
C) 40 cm 
D) 60 cm 
E) 120 cm 
A) 10 cm 
B) 30 cm 
C) 40 cm 
D) 60 cm 
E) 120 cm

Question 20

Sinusoidal water waves are generated in a large ripple tank.The waves travel at 20 cm/s and their adjacent crests are 5.0 cm apart.The time required for each new whole cycle to be generated is:

Accepted Answer

A) 100 s 
B) 4.0 s 
C) 2.0 s 
D) 0.5 s 
E) 0.25 s 
A) 100 s 
B) 4.0 s 
C) 2.0 s 
D) 0.5 s 
E) 0.25 s

Exam 16: Waves

Here are equations for three waves traveling on separate strings.Rank them according to the maximum transverse speed, least to greatest.

A string of length 100 cm is held fixed at both ends and vibrates in a standing wave pattern.The wavelengths of the constituent traveling waves CANNOT be:

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 + t). The speed of the wave is:

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 is:

Two sources, S1 and S2, each emit waves of wavelength λ\lambdaλ in the same medium.The phase difference between the two waves, at the point P shown, is .The quantity π\piπ 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.The angular frequency is:

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 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:

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

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

Two traveling sinusoidal waves interfere to produce a wave with the mathematical form If the value of is appropriately chosen, the two waves might be:

The displacement of an element of a string is given by y(x,t)= 4.3sin, with x in meters and t in seconds.Given that , what is v?

A string, clamped at its ends, vibrates in three segments.The string is 100 cm long.The wavelength is:

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:

For a transverse wave on a string the string displacement is described by y(x,t)= f(x-at)where f is a given function and a is a positive constant.Which of the following does NOT necessarily follow from this statement?

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 30-cm long string, with one end clamped and the other free to move transversely, is vibrating in its second harmonic.The wavelength of the constituent traveling waves is:

Sinusoidal water waves are generated in a large ripple tank.The waves travel at 20 cm/s and their adjacent crests are 5.0 cm apart.The time required for each new whole cycle to be generated is:

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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 + t). The speed of the 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?

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: