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Unformatted text preview: 14.1 WAVE MOTION EXERCISES Section 14.1 Waves and Their Properties 16. Wave crests (adjacent wavefronts) take a time of one period to pass a fixed point, traveling at the wave speed (or phase velocity) for a distance of one wavelength. Thus T v = = = / ( . / ) . . 18 5 3 3 40 m/ m s s 17. INTERPRET This problem is about wave propagation. Given the speed and frequency of the ripples, we are asked to compute the period and the wavelength. DEVELOP Equation 14.1 relates the speed of the wave to its period, frequency, and wavelength: v T f = = This is the equation we shall use to solve the problem. EVALUATE Equation 14.1 gives (a) T f = = = 1 1 5 2 0 192 . . Hz s, and (b) = = = v f 34 5 2 6 54 cm s Hz cm. / . . ASSESS The unit of frequency is Hz, with 1 1 1 Hz s = . If the frequency is kept fixed, then increasing the wavelength will increase the speed of propagation. 18. From Equation 14.1, = = = v f / ( / ) / ( . ) . . 3 10 88 7 10 3 38 8 6 m s Hz m 19. INTERPRET This problem is about wave propagation. Given the speed and frequency of various electromagnetic waves, we are asked to compute their wavelength. DEVELOP Equation 14.1 relates the speed of the wave to its period, frequency, and wavelength: v T f v f = = = This is the equation we shall use to solve the problem. EVALUATE Since the speed of propagation of electromagnetic waves in vacuum is simply equal to the speed of light, v c = = 3 0 10 8 . m/s, Equation 14.1 gives (a) = = = c f 3 10 10 8 6 300 m s Hz m / ; (b) = = = c f 3 10 190 10 8 6 1 58 m s Hz m / . ; (c) = = = = c f 3 10 10 8 10 0 03 3 m s Hz m c m / . ; (d) = = = = c f 3 10 4 10 6 8 13 7 5 10 7 5 m s Hz m m / . . ; (e) = = = = c f 3 10 6 10 7 8 14 5 0 10 500 m s Hz m n m / . ; (f ) = = = = c f 3 10 1 0 10 10 8 18 3 0 10 3 m s Hz o m A / . . (See Appendix C on units.) ASSESS If the speed of propagation is kept fixed, then a higher frequency means a shorter wavelength. 20. The wave speed can be calculated from the distance and the travel time, which, together with the frequency and Equation 14.1, gives a wavelength of = = = = v f d t f / ( / )/ ( . ) . . 1200 5 60 3 1 1 29 km/ km 14 14.2 Chapter 14 Section 14.2 Wave Math 21. INTERPRET This problem is about the ultrasound wave. Given its frequency, and wavelength, we want to find its angular frequency, wave number, and wave speed. DEVELOP The relationships between the speed of the wave, its wave number, frequency, and wavelength are given by Equations 13.6, 14.1, and 14.2: f v T f k = = = = 2 2 , EVALUATE (a) Equation 13.6 gives = = = 2 2 4 8 3 02 10 7 1 f ( . ) . . MHz s (b) Equation 14.2 gives k = = = 2 2 0 31 4 1 2 03 10 ....
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This note was uploaded on 10/21/2010 for the course PHYSICS 2131441 taught by Professor Pheong during the Fall '10 term at University of California, Berkeley.
 Fall '10
 Pheong

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