Version 001 HW#1 - Vibrations and Waves arts (00224) 1

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1 Version HW# - Vibrations and Waves arts (4) This print-out should have 9 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. Superposition 4. points You are given two waves, a transverse wave thatmovestotherightf (x)andatransverse wave that moves to the left f (x), on a string. Astheproblembegins,thewavef (x)ismoving to the right at v + m/s and the wave f (x) is moving to the left at v m/s. v v What is the shape of the wave on the string after s?... correct

2 Version HW# - Vibrations and Waves arts (4) Initial time, t s After s the positions of the two waves are have both moved meters in opposite directions. The sum of the two wave is the resultant wave, the light gray line. Superpostion, at t s Resultant, at t s AP B 998 MC 9. points The initial wave moving to the right is represented withadashed lineandtheeavemoving to the left is represented with a dotted line. One end of a horizontal string is fixed to a wall. A transverse wave pulse in the form of a crest is generated at the other end and moves toward the wall, as shown. Consider the pulse after it has been reflected by the wall.

3 Version HW# - Vibrations and Waves arts (4) v Incident crests reflect as valleys, and vice versa. is/are correct concerning the reflected pulse? A) The reflected pulse forms a valley. B) The reflected pulse forms a crest. C) The reflected pulse has a greater amplitude than that of the incident pulse. D) The reflected pulse has a greater speed than that of the incident pulse.. B and C only Catching a Speeder. points A state trooper s car sends out a radar signal What at a frequency of 8.78 GHz. ind the wavelength of this signal. The wave speed is m/s. Your answer must be within ±.% Correct answer:.4458 m. Let : f 8.78 GHz, and c m/s.. A and D only. A only correct 4. D only 5. C only 6. A, B and D only 7. B only 8. A and B only 9. A and C only. B and D only The speed ofthe pulse isdetermined by the tension of the string and the mass per unit length, and is the same for the incident and reflected pulses. The reflected pulse cannot have an amplitude greater than that of the incident pulse, since no energy is added to the pulse at the wall. There is a phase shift of π at the wall, becausetheendfixedatthewallcannotmove, so the reflected pulse is on the opposite side of the string from the incident pulse, forming a valley. λ c f m/s 8.78 GHz.4458 m. GHz 9 Hz Serway CP 4 4. points A phone cord is 6.64 m long. The cord has a mass of.6 kg. A transverse wave pulse is produced by plucking one end of the taut cord. The pulse makes four trips down and back along the cord in.897 s. What is the tension in the cord? Your answer must be within ±.% Correct answer: 85. N. Let : l 6.64 m, m.6 kg, and t.897 s. Onecompletetripisadistanceofl,sothe speed is v d total 4(l) 8l t t t. The linear density is m l, so v

4 Version HW# - Vibrations and Waves arts (4) 4 v m ( ) 8l 64ml l t ( t) 64(.6 kg)(6.64 m) (.897 s) 85. N. vibrator m.5 g/m 479 kg keywords: Wave on a String 5. points A string is stretched and fixed at both ends, 4 cm apart. If the density of the string is.4 g/cm and its tension is 6 N, what is the speed of the traveling waves? Your answer must be within ±.% Correct answer: m/s. Let :.4 g/cm and 6 N. The speed of a wave in a string is v 6 N.4 g/cm m cm g kg m/s. The length of the string is irrelevant here. keywords: Vibrator and Standing Waves 6. points A 479 kg mass is hung from the end of a string with linear density.5 g/m around a small frictionless peg. A vibrator is attached at a point near the end of the string. or some values of the vibrator s frequency and this mass the string resonates with visible standing waves. The vibrating length of the string is m. What is the frequency that will produce the standing wave shown? The acceleration of gravity is 9.8 m/s. Your answer must be within ±.% Correct answer: 769. Hz. Let : n 4, L m, m 479 kg, and.5 g/m.5 kg/m. A standing wave with n + 5 nodes ( at either end) in the string has a length to wavelength relationship L nλ. Since λ L n and T mg, v f λ T f L mg n f n mg L 4 ( m) 769. s. (479 kg)(9.8 m/s ).5 kg/m Standing Waves 4 7 (part of ). points The length of a string held fixed at both ends is 744 cm and its tension is 6 N. The linear density of the string is.95 kg/m. The string vibrates in six sections; i.e., the string has six antinodes.

5 Version HW# - Vibrations and Waves arts (4) 5 inc the frequency of vibrations in the string. Your answer must be within ±.% Correct answer: Hz. Let : N 6, T 6 N, l 744 cm 7.44 m, and.95 kg/m. When a string is held fixed at each end, the wavelength is λ l N (7.44 m) 6.48 m. The velocity of wave on the string is T v 6 N.95 kg/m 4.9 m/s, 9. points The distance between two nearest nodes of a standing wave is 5 cm. Hand generated pulses move up and down through a complete cycle seven times every eight seconds. ind the velocity of the wave. Your answer must be within ±.% Correct answer:.475 m/s. Let : d 5 cm, n 7, and t 8 s. The distance between two nodes is half the wavelength, so λ d. The frequency is the number of cycles per unit time, so f n t and the velocity is v f λ nd t.475 m/s. (7)(5 cm) 8 s so its frequency is f v λ 4.9 m/s.48 m Hz. 8 (part of ). points What is the fundamental frequency; i.e., the lowest frequency the string can sustain? Your answer must be within ±.% Correct answer:.758 Hz. f f v λ f v l.758 Hz. 4.9 m/s (7.44 m) Standing Waves 9