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1 Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A transverse wave is propagated in a string stretched along the x-axis. The equation of the wave, in SI units, is given by: y = cos π(47t - 17x). The amplitude of the wave, in SI units, is closest to: A) x 17π B) 0.001π C) D) 0.001π/17 E) x 17 1) 2) A transverse wave is propagated in a string stretched along the x-axis. The equation of the wave, in SI units, is given by: y = cos π(46t - 12x). The frequency of the wave, in SI units, is closest to: A) 46 B) 100 C) 69 D) 23 E) 140 2) 3) A transverse wave is propagated in a string stretched along the x-axis. The equation of the wave, in SI units, is given by: y = cos π(38t - 14x). The wave speed, including the sense of direction along the x-axis, in SI units, is closest to: A) 0.37 B) C) -2.7 D) 2.7 E) zero 3) 4) A transverse wave is propagated in a string stretched along the x-axis. The equation of the wave, in SI units, is given by: y = cos π(22t - 16x). The propagation constant of the wave, in SI units, is closest to: A) 8.0 B) 50 C) 32 D) 16 E) 22 4) 5) A transverse wave is propagated in a string stretched along the x-axis. The equation of the wave, in SI units, is given by: y = cos π(52t - 15x). The maximum velocity of a particle on the string, in SI units, is closest to: A) 0.64 B) 0.53 C) 0.43 D) 0.33 E) ) 6) A string, 90 cm long and having a mass of 93 g, is attached to a 730-Hz vibrator at one end. The transverse wave in the string, whose amplitude is 3.0 mm, and that propagates with a velocity of 76 m/s. The energy of the wave is absorbed at the fixed end. In this situation, the propagation constant of the wave, in SI units, is closest to: A) 9.6 B) 48 C) 19 D) 60 E) 30 6) 7) A string, 80 cm long and having a mass of 61 g, is attached to a 660-Hz vibrator at one end. The transverse wave in the string, whose amplitude is 5.0 mm, and that propagates with a velocity of 32 m/s. The energy of the wave is absorbed at the fixed end. In this situation, the tension in the string, in SI units, is closest to: A) 87 B) 78 C) 75 D) 84 E) 81 7) 1

2 8) A string, 30 cm long and having a mass of 14 g, is attached to a 750-Hz vibrator at one end. The transverse wave in the string, whose amplitude is 8.0 mm, and that propagates with a velocity of 54 m/s. The energy of the wave is absorbed at the fixed end. In this situation, the maximum transverse velocity, of a point on the string, in SI units, is closest to: A) 40 B) 35 C) 42 D) 38 E) 33 8) 9) A string, 50 cm long and having a mass of 57 g, is attached to a 910-Hz vibrator at one end. The transverse wave in the string, whose amplitude is 6.0 mm, and that propagates with a velocity of 25 m/s. The energy of the wave is absorbed at the fixed end. In this situation, the average power transmitted by the wave, in SI units, is closest to: A) 2500 B) 5100 C) 3400 D) 4200 E) ) 10) The equation y(x,t) = cos(13.4x + 488t), where all quantities are in SI units, represents a traveling wave having: A) wavelength = m and period = 12.9 ms B) wavelength = 13.4 m and frequency = 488 Hz C) wavelength = m and period = s D) frequency = 488 Hz and period = 12.9 ms E) wavelength = m and frequency = 3060 s 10) 11) Which of the following is a FALSE statement? A) Not all waves are mechanical in nature. B) A wave in which particles move back and forth in the same direction as the wave is moving is called a longitudinal wave. C) The speed of a wave and the speed of the vibrating particles that constitute the wave are different entities. D) In a transverse wave the particle motion is perpendicular to the velocity vector of the wave. E) Waves transport energy and matter from one region to another. 11) 12) A wire, 4.0 m long, with a mass of 60 g, is under tension. A transverse wave is propagated on the wire, for which the frequency is 330 Hz, the wavelength is 0.20 m, and the amplitude is 7.0 mm. The time for a crest of the transverse wave to travel the length of the wire, in ms, is closest to: A) 61 B) 53 C) 82 D) 75 E) 68 12) 13) A wire, 9.0 m long, with a mass of 60 g, is under tension. A transverse wave is propagated on the wire, for which the frequency is 120 Hz, the wavelength is 0.30 m, and the amplitude is 2.3 mm. The tension in the line, in SI units, is closest to: A) 11 B) 13 C) 9.9 D) 14 E) ) 14) A wire, 4.0 m long, with a mass of 20 g, is under tension. A transverse wave is propagated on the wire, for which the frequency is 740 Hz, the wavelength is 0.70 m, and the amplitude is 6.7 mm. The maximum transverse acceleration of a point on a wire, in SI units, is closest to: A) 160,000 B) 130,000 C) 140,000 D) 110,000 E) 90,000 14) 2

3 15) A wave on a stretched string is described in SI units by y = sin (300t - 15x). What is the maximum velocity of a particle on the string? A) 1.20 m/s B) m/s C) 20.0 m/s D) 5.56 m/s 15) E) m/s Figure ) In Fig. 15.1, which of the curves best represents the variation of wave speed as a function of tension for transverse waves on a stretched string? A) A B) B C) C D) D E) E 16) 17) A crane lifts a 2500-kg mass using a steel cable whose mass per unit length is 0.65 kg/m. What is the speed of transverse waves on this cable? A) 578 m/s B) 225 m/s C) 1220 m/s D) 194 m/s E) 1880 m/s 17) 18) A transverse wave traveling along a string transports energy at a rate r. If we want to double this rate, we could A) increase the amplitude by a factor of 2. B) quadruple the amplitude of the wave. C) increase the tension in the string by a factor of 2. D) double the amplitude of the wave. E) double the tension in the string. 18) 3

4 19) A wire of mass 5.00 grams and length 1.20 m is stretched with a tension of 36.0 N. Waves of frequency 50.0 Hz and amplitude 1.6 mm are traveling along the wire. What is the average power carried by the waves? A) W B) W C) W D) W E) W 19) 20) A 2.0-g string, 0.72 m long, is under tension. The string produces a 800-Hz tone when it vibrates in the third harmonic. The speed of sound in air is 344 m/s. In this situation, the wavelength of the standing wave in the string, in SI units, is closest to: A) 0.72 B) 1.1 C) 1.4 D) 0.48 E) ) 21) A 8.0-g string, 0.87 m long, is under tension. The string produces a 900-Hz tone when it vibrates in the third harmonic. The speed of sound in air is 344 m/s. The wavelength of the tone in air, in SI units, is closest to: A) 0.71 B) 0.58 C) 0.87 D) 0.54 E) ) 22) A 3.0-g string, 0.14 m long, is under tension. The string produces a 200-Hz tone when it vibrates in the third harmonic. The speed of sound in air is 344 m/s. The tension in the string, in SI units, is closest to: A) 6.1 B) 4.8 C) 10 D) 8.8 E) ) 23) A string, 0.23 m long, vibrating in the n = 2 harmonic, excites an open pipe, 0.82 m long, into second overtone resonance. The speed of sound in air is 345 m/s. The number of antinodes in the standing wave pattern of the pipe is: A) 6 B) 4 C) 3 D) 5 E) 2 23) 24) A string, 0.17 m long, vibrating in the n = 4 harmonic, excites an open pipe, 0.97 m long, into second overtone resonance. The speed of sound in air is 345 m/s. The number of antinodes in the standing wave pattern of the string is: A) 8 B) 6 C) 7 D) 5 E) 4 24) 25) A string, 0.26 m long, vibrating in the n = 5 harmonic, excites an open pipe, 0.88 m long, into second overtone resonance. The speed of sound in air is 345 m/s. The distance between a node and an adjacent antinode, in the string, in mm, is closest to: A) 26 B) 52 C) 13 D) 260 E) 39 25) 26) A string, 0.25 m long, vibrating in the n = 6 harmonic, excites an open pipe, 0.96 m long, into second overtone resonance. The speed of sound in air is 345 m/s. The common resonant frequency of the string and the pipe, in SI units, is closest to: A) 700 B) 540 C) 360 D) 450 E) ) 4

5 27) A string, 0.28 m long, vibrating in the n = 3 harmonic, excites an open pipe, 0.82 m long, into second overtone resonance. The speed of sound in air is 345 m/s. The velocity of transverse waves in the string, in SI units, is closest to: A) 98 B) 100 C) 110 D) 91 E) ) 28) At one instant of time two transverse waves are traveling in the same direction along a stretched string. They are described in SI units by y 1 = 0.05 cos 5x and y 2 = 0.05 sin 5x How far from the origin is the nearest crest of the composite wave? A) 0.63 m B) 0.31 m C) 0.20 m D) 0.10 m E) 0.16 m 28) 29) An ocean wave directed straight in strikes a seawall perpendicularly to its path and is reflected. The incoming wave travels 0.86 m/s and has a period of 6.9 s. The wave has an antinode at the wall. How far from the wall is the nearest node in the standing wave setup? A) 1.2 m B) 0.74 m C) 2.2 m D) 1.5 m E) 1.1 m 29) 30) What is the period of the wave described in SI units by y = 1.1 sin (324 t - 13x)? A) 483 ms B) 76.9 ms C) 1.49 ms D) 19.4 ms E) 3.09 ms 30) Situation 15.1 A mass m is hung from the ceiling by a thin 8.25-g wire that is 65.0 cm long. When you gently pluck the upper end of the wire, a pulse travels down the wire and returns 7.84 ms later, having reflected off the lower end. The speed of sound in the room is 344 m/s, and m is great enough to prevent the lower end of the wire from moving. 31) In Situation 15.1, mass m is closest to: A) 8.90 kg B) 35.6 kg C) 23.1 kg D) 349 kg E) 227 kg 31) 32) In Situation 15.1, if the wire is vibrating in its second overtone, the frequency of the sound it will produce is closest to: A) 765 Hz B) 128 Hz C) 255 Hz D) 383 Hz E) 191 Hz 32) 33) In Situation 15.1, if the wire is vibrating in its second overtone, the wavelength of the sound it will produce is closest to: A) m B) m C) m D) 1.35 m E) m 33) 34) In Situation 15.1, if the wavelength of the standing wave for a given vibrational mode of the wire is!, what will be the wavelength in the same mode if the mass m is doubled without stretching the wire? A) 2! B)! C)!/ 2 D)!/2 E) 2! 34) 35) In Situation 15.1, if the frequency of the standing wave for a given vibrational mode of the wire is f, what will be the frequency in the same mode if the mass m is doubled without stretching the wire? A) f/ 2 B) f/2 C) 2 f D) f E) 2 f 35) 5

6 36) What is the frequency of the fundamental mode of vibration of a steel piano wire stretched to a tension of 440 N? The wire is m long and has a mass of 5.60 grams. A) 366 Hz B) 234 Hz C) 312 Hz D) 295 Hz E) 517 Hz 36) 37) Two violinists are trying to tune their instruments in an orchestra. One is producing the desired frequency, 440 Hz. The other is producing a frequency of Hz. By what percentage should the out-of-tune musician change the tension in his string to bring his instrument into tune at 440 Hz? A) 1.0% B) 0.6% C) 2.0% D) 4.0% E) 0.5% 37) SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 38) The equation of a certain traveling transverse wave is y(x,t) = 9.00 sin(83.00πt πx), where t is in seconds and x and y are in centimeters. Find the speed of propagation, the period, and wavelength for these waves. (Express your answer in SI units.) 38) 39) In a given situation transverse waves on a string carry an average power of 88 watts. What does the average power carried by the waves become if (a) the amplitude of the waves is increased from 5.0 cm to 48 cm while the frequency and wave speed are held fixed, or (b) the tension with which the string is stretched is increased from 5.0 N to 39 N while the frequency and amplitude of the waves is held fixed? 39) 40) Standing waves of frequency 96 Hz are produced on a string that has mass per unit length kg/m. With what tension must the string be stretched between two supports if adjacent nodes in the standing wave are to be 0.67 meters apart? 40) 41) A thin steel wire with Young's modulus of 2.00 x Pa and density kg/m 3 is stretched between two supports with tension N. If the radius of the wire is m, find the ratio of the speed of longitudinal waves to the speed of transverse waves in the wire. 42) A tiny vibrating source sends waves uniformly in all directions. An area of 3.25 cm 2 on a sphere of radius 2.50 m centered on the source receives energy at a rate of 4.20 J/s. (a) What is the intensity of the waves at 2.50 m from the source and at 10.0 m from the source? (b) At what rate is energy leaving the vibrating source of the waves? 41) 42) 6

7 Answer Key Testname: UNTITLED2 1) C 2) D 3) D 4) B 5) D 6) D 7) B 8) D 9) E 10) A 11) E 12) A 13) E 14) C 15) A 16) B 17) D 18) A 19) E 20) D 21) E 22) E 23) B 24) E 25) A 26) B 27) E 28) E 29) D 30) D 31) B 32) D 33) E 34) B 35) C 36) D 37) C 38) speed = m/s period = s wavelength = m 39) (a) 8100 watts (b) 250 watts 40) 260 N 41) ) (a) 12,900 W/m 2 (at 2.50 m), 808 W/m 2 (at 10.0 m) (b) W 7

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