Deck 16: Waves
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Deck 16: Waves
1
What are the three main types of waves?
A)transverse, longitudinal, linear
B)plane, spherical, transverse
C)mechanical, electromagnetic, matter
D)transverse, linear, water
E)plane, longitudinal, mechanical
A)transverse, longitudinal, linear
B)plane, spherical, transverse
C)mechanical, electromagnetic, matter
D)transverse, linear, water
E)plane, longitudinal, mechanical
mechanical, electromagnetic, matter
2
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
is given by tan 11ef007b_a973_2e1e_bc85_7b3bfc1d1daa_TB6585_11 =:
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)


3
A traveling sinusoidal wave is shown below.At which point is the motion 180 out of phase with the motion at point P? 
A)A
B)B
C)C
D)D
E)E

A)A
B)B
C)C
D)D
E)E
C
4
In the diagram below, the interval PQ represents: 
A)wavelength/2
B)wavelength
C)2 x amplitude
D)period/2
E)period

A)wavelength/2
B)wavelength
C)2 x amplitude
D)period/2
E)period
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5
Two waves are traveling on two different strings.The displacement of one is given by y1(x,t)= ymsin(kx + t)and of the other by y2(x,t)= ymsin(kx + t + φ).What is the difference between these two waves?
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.
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6
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)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.
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7
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 period of the wave? 
A)A
B)B
C)C
D)D
E)E

A)A
B)B
C)C
D)D
E)E
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8
A sinusoidal wave is traveling toward the right as shown.Which letter correctly labels the wavelength of the wave? 
A)A
B)B
C)C
D)D
E)E

A)A
B)B
C)C
D)D
E)E
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9
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:
A)0°
B)90°
C)135°
D)180°
E)270°


A)0°
B)90°
C)135°
D)180°
E)270°
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10
A sinusoidal wave is traveling toward the right as shown.Which letter correctly labels the amplitude of the wave? 
A)A
B)B
C)C
D)D
E)E

A)A
B)B
C)C
D)D
E)E
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11
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:
A)0.10 rad/m
B)3 rad/m
C)10 rad/m
D)10 rad/m
E)3.0 rad/m
A)0.10 rad/m
B)3 rad/m
C)10 rad/m
D)10 rad/m
E)3.0 rad/m
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12
What is the difference between transverse and longitudinal waves?
A)Mechanical waves are transverse waves while electromagnetic waves are longitudinal.
B)Plane waves are transverse waves while spherical waves are longitudinal.
C)Only longitudinal waves transmit matter.
D)Only transverse waves transmit energy.
E)In transverse waves the displacement is perpendicular to the direction of propagation of the wave, while in longitudinal waves the displacement is parallel to the direction of propagation.
A)Mechanical waves are transverse waves while electromagnetic waves are longitudinal.
B)Plane waves are transverse waves while spherical waves are longitudinal.
C)Only longitudinal waves transmit matter.
D)Only transverse waves transmit energy.
E)In transverse waves the displacement is perpendicular to the direction of propagation of the wave, while in longitudinal waves the displacement is parallel to the direction of propagation.
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13
Three traveling sinusoidal waves are on identical strings, with the same tension.The mathematical forms of the waves are y1(x,t)= ymsin(3x - 6t), y2(x,t)= ymsin(4x - 8t), and y3(x,t)= ymsin(6x - 12t), where x is in meters and t is in seconds.Match each mathematical form to the appropriate graph below. 
A)y1: i, y2: ii, y3: iii
B)y1: iii, y2: ii, y3: i
C)y1:i, y2: iii, y3: ii
D)y1: ii, y2: i, y3: iii
E)y1: iii, y2: i, y3: ii

A)y1: i, y2: ii, y3: iii
B)y1: iii, y2: ii, y3: i
C)y1:i, y2: iii, y3: ii
D)y1: ii, y2: i, y3: iii
E)y1: iii, y2: i, y3: ii
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14
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? 
A)A
B)B
C)C
D)D
E)E

A)A
B)B
C)C
D)D
E)E
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15
The displacement of a string is given by y(x,t)= ymsin(kx +
t).
The speed of the wave is:
A)"2 k/
0"
B)"11ef007c_d3c5_9274_bc85_fb68333484e4_TB6585_11 /k"
C)" 11ef007c_d3c5_9274_bc85_fb68333484e4_TB6585_11 k"
D)"2 /k"
E)"k/2 "

The speed of the wave is:
A)"2 k/

B)"11ef007c_d3c5_9274_bc85_fb68333484e4_TB6585_11 /k"
C)" 11ef007c_d3c5_9274_bc85_fb68333484e4_TB6585_11 k"
D)"2 /k"
E)"k/2 "
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16
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)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
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17
The displacement of a string is given by
The wavelength of the wave is:
A)"2
"
B)"k/ 11ef007c_d3c5_9274_bc85_fb68333484e4_TB6585_11 "
C)" 11ef007c_d3c5_9274_bc85_fb68333484e4_TB6585_11 k"
D)"2 /k"
E)"k/2 "

A)"2

B)"k/ 11ef007c_d3c5_9274_bc85_fb68333484e4_TB6585_11 "
C)" 11ef007c_d3c5_9274_bc85_fb68333484e4_TB6585_11 k"
D)"2 /k"
E)"k/2 "
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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?
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
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19
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
is:
A)45°
B)90°
C)135°
D)180°
E)270°


A)45°
B)90°
C)135°
D)180°
E)270°
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20
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:
A)0.10 rad/s
B)3.0 rad/s
C)10 rad/s
D)20 rad/s
E)10 rad/s
A)0.10 rad/s
B)3.0 rad/s
C)10 rad/s
D)20 rad/s
E)10 rad/s
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21
A transverse wave travels on a string of length 1.3 m and diameter 1.1 mm, whose mass is 10 g and which is under a tension of 16 N.What is the linear mass density of the string?
A)7.7 x 10-3 kg/m
B)0.13 kg/m
C)7.7 kg/m
D)46 kg/m
E)130 kg/m
A)7.7 x 10-3 kg/m
B)0.13 kg/m
C)7.7 kg/m
D)46 kg/m
E)130 kg/m
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22
For a given medium, the frequency of a wave is:
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
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23
Let f be the frequency, v the speed, and T the period of a sinusoidal traveling wave.The correct relationship is:
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
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24
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 -
t -
), what is the phase constant 11ef007d_9e11_e6f7_bc85_cd56af2ad619_TB6585_11 
A)0
B) /6
C) /4
D) /2
E)3 /2



A)0
B) /6
C) /4
D) /2
E)3 /2
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25
A source of frequency f sends waves of wavelength traveling with speed v in some medium.If the frequency is changed from f to 2f, then the new wavelength and new speed are (respectively):
A)"2 , v"
B)" /2, v"
C)" , 2v"
D)" , v/2"
E)" /2, 2v"
A)"2 , v"
B)" /2, v"
C)" , 2v"
D)" , v/2"
E)" /2, 2v"
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26
A transverse traveling sinusoidal wave on a string has a frequency of 100 Hz, a wavelength of 0.040 m and an amplitude of 2.0 mm.The maximum velocity of any point on the string is:
A)0.20 m/s
B)1.3 m/s
C)4.0 m/s
D)15 m/s
E)25 m/s
A)0.20 m/s
B)1.3 m/s
C)4.0 m/s
D)15 m/s
E)25 m/s
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27
The mathematical forms for the three sinusoidal traveling waves are given by
where x is in meters and t is in seconds.Of these waves:
A)wave 1 has the greatest wave speed and the greatest maximum transverse string speed
B)wave 2 has the greatest wave speed and wave 1 has the greatest maximum transverse string speed
C)wave 3 has the greatest wave speed and the greatest maximum transverse string speed
D)wave 2 has the greatest wave speed and wave 3 has the greatest maximum transverse string speed
E)wave 3 has the greatest wave speed and wave 2 has the greatest maximum transverse string speed

A)wave 1 has the greatest wave speed and the greatest maximum transverse string speed
B)wave 2 has the greatest wave speed and wave 1 has the greatest maximum transverse string speed
C)wave 3 has the greatest wave speed and the greatest maximum transverse string speed
D)wave 2 has the greatest wave speed and wave 3 has the greatest maximum transverse string speed
E)wave 3 has the greatest wave speed and wave 2 has the greatest maximum transverse string speed
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28
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)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)
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29
Here are equations for three waves traveling on separate strings.Rank them according to the maximum transverse speed, least to greatest. 
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
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30
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: 
A)
B)
C)
D) "
"
E)"no direction since v = 0"

A)
B)
C)
D) "

E)"no direction since v = 0"
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31
A sinusoidal transverse wave is traveling on a string.Any point on the string:
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
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32
Let f be the frequency, v the speed, and T the period of a sinusoidal traveling wave.The angular frequency is given by:
A)1/T
B)2 /T
C)vT
D)f/T
E)T/f
A)1/T
B)2 /T
C)vT
D)f/T
E)T/f
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33
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)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)

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34
A transverse traveling sinusoidal wave on a string has a frequency of 100 Hz, a wavelength of 0.040 m and an amplitude of 2.0 mm.The maximum acceleration of any point on the string is:
A)0 m/s2
B)200 m/s2
C)390 m/s2
D)790 m/s2
E)1600 m/s2
A)0 m/s2
B)200 m/s2
C)390 m/s2
D)790 m/s2
E)1600 m/s2
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35
Water waves in the sea are observed to have a wavelength of 300 m and a frequency of 0.07 Hz.The speed of these waves is:
A)0.00023 m/s
B)2.1 m/s
C)21 m/s
D)4300 m/s
E)none of these
A)0.00023 m/s
B)2.1 m/s
C)21 m/s
D)4300 m/s
E)none of these
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36
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:
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
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37
Any point on a string carrying a sinusoidal wave is moving with its maximum speed when:
A)the magnitude of its acceleration is a maximum
B)the magnitude of its displacement is a maximum
C)the magnitude of its displacement is a minimum
D)the magnitude of its displacement is half the amplitude
E)the magnitude of its displacement is one fourth the amplitude
A)the magnitude of its acceleration is a maximum
B)the magnitude of its displacement is a maximum
C)the magnitude of its displacement is a minimum
D)the magnitude of its displacement is half the amplitude
E)the magnitude of its displacement is one fourth the amplitude
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38
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:
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
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39
A wave traveling to the right on a stretched string is shown below.The direction of the instantaneous velocity of the point P on the string is: 
A)
B)
C)
D) "
E)"no direction since v = 0"

A)
B)
C)
D) "

E)"no direction since v = 0"
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40
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.
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)
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41
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)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
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42
The sum of two sinusoidal traveling waves is a sinusoidal traveling wave only if:
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
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43
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.
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
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44
Two separated sources emit sinusoidal traveling waves that have the same wavelength and are in phase at their respective sources.One travels a distance 1 to get to the observation point while the other travels a distance 2.The amplitude is a minimum at the observation point if 1 2 is:
A)an odd multiple of /2
B)an odd multiple of /4
C)a multiple of .
D)an odd multiple of /2.
E)a multiple of
A)an odd multiple of /2
B)an odd multiple of /4
C)a multiple of .
D)an odd multiple of /2.
E)a multiple of
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45
Fully constructive interference between two sinusoidal waves of the same frequency occurs only if they:
A)travel in the same direction and are 270°out of phase
B)travel in the same direction and are 45° out of phase
C)travel in the same direction and are in phase
D)travel in the same direction and are 180° out of phase
E)travel in the same direction and are 90° out of phase
A)travel in the same direction and are 270°out of phase
B)travel in the same direction and are 45° out of phase
C)travel in the same direction and are in phase
D)travel in the same direction and are 180° out of phase
E)travel in the same direction and are 90° out of phase
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46
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:
A)the frequency decreases by a factor of 4
B)the frequency decreases by a factor of 2
C)the wave speed decreases by a factor of 4
D)the wave speed decreases by a factor of 2
E)the wave speed 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 wave speed decreases by a factor of 4
D)the wave speed decreases by a factor of 2
E)the wave speed increases by a factor of 2
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47
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 ° , the amplitude of the resultant wave is given by
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
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48
Two sinusoidal waves travel in the same direction and have the same frequency.Their amplitudes are y1m and y2m.The smallest possible amplitude of the resultant wave is:
A)
B)
C)
D)
E)
A)

B)

C)

D)

E)

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49
A stretched string, clamped at its ends, vibrates at a particular frequency.To double that frequency, one can change the string tension by a factor of:
A)2
B)4
C)
D)1/2
E)
A)2
B)4
C)

D)1/2
E)

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50
The speed of a sinusoidal wave on a string depends on:
A)the frequency of the wave
B)the wavelength of the wave
C)the length of the string
D)the tension in the string
E)the amplitude of the wave
A)the frequency of the wave
B)the wavelength of the wave
C)the length of the string
D)the tension in the string
E)the amplitude of the wave
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51
The diagram shows three identical strings that have been put under tension by suspending masses of 5 kg each.For which is the wave speed the greatest? 
A)1
B)2
C)3
D)1 and 3 tie
E)2 and 3 tie

A)1
B)2
C)3
D)1 and 3 tie
E)2 and 3 tie
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52
Two identical but separate strings, with the same tension, carry sinusoidal waves with the same frequency.Wave A has an amplitude that is twice that of wave B and transmits energy at a rate that is __________ that of wave B.
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
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53
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:
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
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54
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:
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
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55
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)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
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56
Fully destructive interference between two sinusoidal waves of the same frequency and amplitude occurs only if they:
A)travel in the same direction and are 270 ° out of phase
B)travel in the same direction and are 45 ° out of phase
C)travel in the same direction and are in phase
D)travel in the same direction and are 180 ° out of phase
E)travel in the same direction and are 90 ° out of phase
A)travel in the same direction and are 270 ° out of phase
B)travel in the same direction and are 45 ° out of phase
C)travel in the same direction and are in phase
D)travel in the same direction and are 180 ° out of phase
E)travel in the same direction and are 90 ° out of phase
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57
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:
A)
B)
C)
D)
E)


A)

B)

C)

D)

E)

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58
Three separate strings are made of the same material.String 1 has length L and tension
, string 2 has length 2L and tension 2 11ef007d_c3e4_5de8_bc85_0d43416ecdc2_TB6585_11 and string 3 has length 3L and tension 3 11ef007d_c3e4_5de8_bc85_0d43416ecdc2_TB6585_11 .A pulse is started at one end of each string.If the pulses start at the same time, the order in which they reach the other end is:
A)1, 2, 3
B)3, 2, 1
C)2, 3, 1
D)3, 1, 2
E)they all take the same time

A)1, 2, 3
B)3, 2, 1
C)2, 3, 1
D)3, 1, 2
E)they all take the same time
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59
A sinusoidal wave is generated by moving the end of a string up and down periodically.The generator does not supply any power when the end of the string
A)has its least 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 least acceleration
B)has its greatest displacement
C)has half its greatest displacement
D)has one fourth its greatest displacement
E)has its least displacement
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60
The time required for a small pulse to travel from A to B on a stretched cord shown is NOT altered by changing:
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)
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61
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:
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
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62
A standing wave pattern is established in a string as shown.The wavelength of one of the component traveling waves is: 
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
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63
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?
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
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64
When a certain string is clamped at both ends, the lowest four resonant frequencies are measured to be 100, 150, 200, and 250 Hz.One of the resonant frequencies (below 200 Hz)is missing.What is it?
A)25 Hz
B)50 Hz
C)75 Hz
D)125 Hz
E)225 Hz
A)25 Hz
B)50 Hz
C)75 Hz
D)125 Hz
E)225 Hz
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65
Which of the following represents the motion of a string element at an antinode of a standing wave?
A)y = (6.0 mm)sin[(3.0 m-1)x + (2.0 s-1)t]
B)y = (6.0 mm)cos[(3.0 m-1)x - (2.0 s-1)t]
C)y = (6.0 mm)cos[(3.0 m-1)x + (2.0 s-1)t]
D)y = (6.0 mm)sin[(3.0 m-1)x
E)y = (6.0 mm)cos[(2.0 s-1)t
A)y = (6.0 mm)sin[(3.0 m-1)x + (2.0 s-1)t]
B)y = (6.0 mm)cos[(3.0 m-1)x - (2.0 s-1)t]
C)y = (6.0 mm)cos[(3.0 m-1)x + (2.0 s-1)t]
D)y = (6.0 mm)sin[(3.0 m-1)x
E)y = (6.0 mm)cos[(2.0 s-1)t
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66
Two traveling waves, y1 = A sin[k(x - vt)] and y2 = A sin[k(x + vt)], are superposed on the same string.The distance between the adjacent nodes is:
A)"vt/ "
B)"vt/2 "
C)" /2k"
D)" /k"
E)"2 /k"
A)"vt/ "
B)"vt/2 "
C)" /2k"
D)" /k"
E)"2 /k"
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67
A wave on a stretched string is reflected from a fixed end P of the string.The phase difference, at P, between the incident and reflected waves is:
A)"0 rad"
B)" rad"
C)" /2 rad"
D)"depends on the velocity of the wave"
E)"depends on the frequency of the wave"
A)"0 rad"
B)" rad"
C)" /2 rad"
D)"depends on the velocity of the wave"
E)"depends on the frequency of the wave"
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68
Two sources, S1 and S2, each emit waves of wavelength in the same medium.The phase difference between the two waves, at the point P shown, is
.The quantity is: 
A)"the distance S1S2"
B)"the angle S1PS2"
C)" /2"
D)"the phase difference between the two sources"
E)"zero for transverse waves, for longitudinal waves"


A)"the distance S1S2"
B)"the angle S1PS2"
C)" /2"
D)"the phase difference between the two sources"
E)"zero for transverse waves, for longitudinal waves"
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69
A standing 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
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
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70
Which of the following represents a standing wave?
A)y = (6.0 mm)sin[(3.0 m-1)x + (2.0 s-1)t] - (6.0 mm)cos[(3.0 m-1)x + 2.0]
B)y = (6.0 mm)cos[(3.0 m-1)x - (2.0 s-1)t] + (6.0 mm)cos[(2.0 s-1)t + (3.0 m-1)x]
C)y = (6.0 mm)cos[(3.0 m-1)x - (2.0 s-1)t] - (6.0 mm)sin[(2.0 s-1)t - 3.0]
D)y = (6.0 mm)sin[(3.0 m-1)x - (2.0 s-1)t] - (6.0 mm)cos[(2.0 s-1)t + (3.0 m-1)x]
E)y = (6.0 mm)sin[(3.0 m-1)x] + (6.0 mm)cos[(2.0 s-1)t]
A)y = (6.0 mm)sin[(3.0 m-1)x + (2.0 s-1)t] - (6.0 mm)cos[(3.0 m-1)x + 2.0]
B)y = (6.0 mm)cos[(3.0 m-1)x - (2.0 s-1)t] + (6.0 mm)cos[(2.0 s-1)t + (3.0 m-1)x]
C)y = (6.0 mm)cos[(3.0 m-1)x - (2.0 s-1)t] - (6.0 mm)sin[(2.0 s-1)t - 3.0]
D)y = (6.0 mm)sin[(3.0 m-1)x - (2.0 s-1)t] - (6.0 mm)cos[(2.0 s-1)t + (3.0 m-1)x]
E)y = (6.0 mm)sin[(3.0 m-1)x] + (6.0 mm)cos[(2.0 s-1)t]
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71
Standing waves are produced by the interference of two traveling sinusoidal waves, each of frequency 100 Hz.The distance from the 2nd node to the 5th node is 60 cm.The wavelength of each of the two original waves is:
A)50 cm
B)40 cm
C)30 cm
D)20 cm
E)15 cm
A)50 cm
B)40 cm
C)30 cm
D)20 cm
E)15 cm
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72
A 40-cm long string, with one end clamped and the other free to move transversely, is vibrating in its fundamental standing wave mode.The wavelength of the constituent traveling waves is:
A)10 cm
B)20 cm
C)40 cm
D)80 cm
E)160 cm
A)10 cm
B)20 cm
C)40 cm
D)80 cm
E)160 cm
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73
A wave on a string is reflected from a fixed end.The reflected wave:
A)is in phase with the original wave at the end
B)is 180 ° out of phase with the original wave at the end
C)has a larger amplitude than the original wave
D)has a larger speed than the original wave
E)cannot be transverse
A)is in phase with the original wave at the end
B)is 180 ° out of phase with the original wave at the end
C)has a larger amplitude than the original wave
D)has a larger speed than the original wave
E)cannot be transverse
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74
If 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)" /4"
B)" /2"
C)"3 /4"
D)" "
E)"2 "
A)" /4"
B)" /2"
C)"3 /4"
D)" "
E)"2 "
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75
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:
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
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76
A string of length L is clamped at each end and vibrates in a standing wave pattern.The wavelengths of the constituent traveling waves CANNOT be:
A)L
B)2L
C)L/2
D)2L/3
E)4L
A)L
B)2L
C)L/2
D)2L/3
E)4L
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77
The sinusoidal wave y(x,t)= ymsin(kx -
t)
Is incident on the fixed end of a string at x = L.The reflected wave is given by:
A)ymsin(kx + 11ef007f_5806_c585_bc85_4919ea62275a_TB6585_11 t)
B)-ymsin(kx + 11ef007f_5806_c585_bc85_4919ea62275a_TB6585_11 t)
C)ymsin(kx + 11ef007f_5806_c585_bc85_4919ea62275a_TB6585_11 t - kL)
D)ymsin(kx + 11ef007f_5806_c585_bc85_4919ea62275a_TB6585_11 t - 2kL)
E)-ymsin(kx + 11ef007f_5806_c585_bc85_4919ea62275a_TB6585_11 t + 2kL)

Is incident on the fixed end of a string at x = L.The reflected wave is given by:
A)ymsin(kx + 11ef007f_5806_c585_bc85_4919ea62275a_TB6585_11 t)
B)-ymsin(kx + 11ef007f_5806_c585_bc85_4919ea62275a_TB6585_11 t)
C)ymsin(kx + 11ef007f_5806_c585_bc85_4919ea62275a_TB6585_11 t - kL)
D)ymsin(kx + 11ef007f_5806_c585_bc85_4919ea62275a_TB6585_11 t - 2kL)
E)-ymsin(kx + 11ef007f_5806_c585_bc85_4919ea62275a_TB6585_11 t + 2kL)
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78
Two sinusoidal waves, each of wavelength 5 m and amplitude 10 cm, travel in opposite directions on a 20-m stretched string which is clamped at each end.Excluding the nodes at the ends of the string, how many nodes appear in the resulting standing wave?
A)3
B)4
C)5
D)7
E)8
A)3
B)4
C)5
D)7
E)8
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79
When a string is vibrating in a standing wave pattern the power transmitted across an antinode, compared to the power transmitted across a node, is:
A)more
B)less
C)the same (zero)
D)the same (non-zero)
E)sometimes more, sometimes less, and sometimes the same
A)more
B)less
C)the same (zero)
D)the same (non-zero)
E)sometimes more, sometimes less, and sometimes the same
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80
Two separated sources emit sinusoidal traveling waves that have the same wavelength and are in phase at their respective sources.One travels a distance 1 to get to the observation point while the other travels a distance 2 The amplitude is a maximum at the observation point if 1 2 is:
A)an odd multiple of /2
B)an odd multiple of /4
C)a multiple of
D)an odd multiple of /2
E)a multiple of
A)an odd multiple of /2
B)an odd multiple of /4
C)a multiple of
D)an odd multiple of /2
E)a multiple of
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