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The vertical displacement of a string is given by y(x,t) = (6.00 mm) cos[(3.25 m-1) x - (7.22 s-1) t]. What is the speed of the wave?


A) 0.450 m/s
B) 1.41 m/s
C) 2.22 m/s
D) 3.16 m/s
E) 23.5 m/s

F) D) and E)
G) A) and D)

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An earthquake generates three kinds of waves: surface waves (L-waves) , which are the slowest and weakest, shear (S) waves, which are transverse waves and carry most of the energy, and pressure (P) waves, which are longitudinal waves and are the fastest. People do not generally feel the P waves, but animals seem to be sensitive to them. Take the density of the material through which these waves travel to be 2.0 × 103 kg/m3, the Young's modulus to be 9.8 × 1010 N/m2, and the shear modulus to be 3.2 × 1010 N/m2. A person reports that her dog started barking 30 seconds "before the earthquake." Approximately how far away was the origin of the earthquake?


A) 180 km
B) 280 km
C) 140 km
D) 90 km
E) 360 km

F) B) and C)
G) None of the above

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The velocity of a transverse wave on a stretched string or cord depends only on the tension in the cord.

A) True
B) False

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Four waves are described by the following expressions, where distances are measured in meters and times in seconds. I y = 0.12 cos(3x - 21t) II y = 0.15 sin(6x + 42t) III y = 0.13 cos(6x + 21t) IV y = -0.23 sin(3x - 42t) Which of these waves have the same period?


A) I and III, and also II and IV
B) I and IV, and also II and III
C) I and II, and also III and IV
D) All of them have the same period.
E) They all have different periods.

F) A) and B)
G) A) and D)

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The speed of waves on a thin wire is 150 m/s. The density of the material that the wire is made of is 5000 kg/m3. The wire has a 0.500 mm diameter circular crosssection. What is the tension that the wire is under?


A) 76.2 N
B) 22.1 N
C) 88.4 N
D) 0.147 N
E) 56.7 N

F) All of the above
G) D) and E)

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A small town has decided to forego the use of electrical power and send energy through town via mechanical waves on ropes. They use rope with a mass per length of 1.50 kg/m under 6000 N tension. If they are limited to a wave amplitude of 0.500 m, what must be the frequency of waves necessary to transmit power at the average rate of 2.00 kW?


A) 24.8 Hz
B) 169 Hz
C) 60.0 Hz
D) 2.07 Hz
E) 2.00 kHz

F) B) and E)
G) D) and E)

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Describe the phenomenon known as refraction

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When any wave strikes a boundary, some o...

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The energy transported by a wave is proportional to the amplitude of the wave.

A) True
B) False

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Which of the following is a solution to the wave equation: Which of the following is a solution to the wave equation:   A) z(x,t)  = Acos[k(x - Ct) ] B) z(x,t)  = Acos[k(x - C<sup>2</sup><sup>t</sup>) ] C) z(x,t)  = Acos[k(x - t/C) ] D) z(x,t)  = Acos[k(x -   t) ] E) z(x,t)  = Acos[k(x - t/   ) ]


A) z(x,t) = Acos[k(x - Ct) ]
B) z(x,t) = Acos[k(x - C2t) ]
C) z(x,t) = Acos[k(x - t/C) ]
D) z(x,t) = Acos[k(x - Which of the following is a solution to the wave equation:   A) z(x,t)  = Acos[k(x - Ct) ] B) z(x,t)  = Acos[k(x - C<sup>2</sup><sup>t</sup>) ] C) z(x,t)  = Acos[k(x - t/C) ] D) z(x,t)  = Acos[k(x -   t) ] E) z(x,t)  = Acos[k(x - t/   ) ] t) ]
E) z(x,t) = Acos[k(x - t/ Which of the following is a solution to the wave equation:   A) z(x,t)  = Acos[k(x - Ct) ] B) z(x,t)  = Acos[k(x - C<sup>2</sup><sup>t</sup>) ] C) z(x,t)  = Acos[k(x - t/C) ] D) z(x,t)  = Acos[k(x -   t) ] E) z(x,t)  = Acos[k(x - t/   ) ] ) ]

F) D) and E)
G) C) and D)

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Periodic waves with a period of 0.026 s travel along a rod at 1200 m/s. What is the wave number k of the waves?


A) 5.0 m-1
B) 31 m-1
C) 6.9 m-1
D) 0.20 m-1
E) 68 m-1

F) A) and D)
G) All of the above

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At a location that is 3.00 m from wave source A and 4.20 m from wave source B, destructive interference occurs. Source A and source B are coherent and in phase. What is the maximum wavelength of the waves?


A) 0.60 m
B) 1.20 m
C) 12.6 m
D) 1.40 m
E) 2.40 m

F) A) and E)
G) A) and C)

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FIGURE 15-1 FIGURE 15-1   -In Fig. 15-1, the wavelength is A) 8 m. B) 4 m. C) 2 m. D) 1 m. E) cannot be determined from the given information. -In Fig. 15-1, the wavelength is


A) 8 m.
B) 4 m.
C) 2 m.
D) 1 m.
E) cannot be determined from the given information.

F) None of the above
G) A) and E)

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Two waves travel simultaneously through the same medium. The first wave is described by y1(x,t) = (2.00 cm) cos[kx-ωt] and the second wave by y2(x,t) = (3.00 cm) sin(kx-ωt) . What is the amplitude of the resulting wave?


A) 1.00 cm
B) 2.50 cm
C) 3.61 cm
D) 5.00 cm
E) 3.94 cm

F) None of the above
G) A) and E)

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State the principle of superposition.

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When two or more waves pass th...

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Describe the phenomenon known as diffraction.

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Waves spread as they travel. When they e...

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Two wave pulses pass each other on a string. The one traveling toward the right has a positive amplitude, while the one traveling toward the left has an equal amplitude in the negative direction. At the point that they occupy the same region of space at the same time


A) constructive interference occurs.
B) destructive interference occurs.
C) a standing wave is produced.
D) a traveling wave is produced.
E) a wave pulse is produced.

F) B) and D)
G) A) and B)

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FIGURE 15-2 FIGURE 15-2     -A harmonic wave has a wavelength of 2.0 m and a frequency of 5.0 Hz. What is the speed of the wave? A) 10 m/s B) 0.40 m/s C) 0.50 m/s D) 0.10 m/s E) 2.5 m/s FIGURE 15-2     -A harmonic wave has a wavelength of 2.0 m and a frequency of 5.0 Hz. What is the speed of the wave? A) 10 m/s B) 0.40 m/s C) 0.50 m/s D) 0.10 m/s E) 2.5 m/s -A harmonic wave has a wavelength of 2.0 m and a frequency of 5.0 Hz. What is the speed of the wave?


A) 10 m/s
B) 0.40 m/s
C) 0.50 m/s
D) 0.10 m/s
E) 2.5 m/s

F) A) and B)
G) None of the above

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What is the period of a wave described by the following function? y(x,t) = (2.00 m) cos[(6.00 m-1) x + (10.00 s-1) t] + (2.00 m) cos[(3.00 m-1) x + (5.00 s-1) t]


A) 0.628 s
B) 5.00 s
C) 1.26 s
D) 10.0 s
E) This is not a periodic function, so it does not have a period.

F) A) and B)
G) C) and E)

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The velocity of a longitudinal wave traveling in a liquid or a gas depends only on the density of the fluid.

A) True
B) False

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A wave has a period 2.00 s, an amplitude 20.0 cm, and a wavelength 3.00 m. What is the speed of the wave?


A) 10.0 cm/s
B) 1.50 m/s
C) 340 m/s
D) 0.100 cm/s
E) 0.667 m/s

F) D) and E)
G) A) and E)

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