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# CALC (a) Show that for a wave on a string, the kinetic ISBN: 9780321675460 31

## Solution for problem 85CP Chapter 15

University Physics | 13th Edition

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Problem 85CP

CALC ?(a) Show that for a wave on a string, the kinetic energy per unit length of string is where is the mass per unit length. (b) Calculate for a sinusoidal wave given by Eq. (15.7). (c) There is also elastic potential energy in the string, associated with the work required to deform and stretch the string. Consider a short segment of string at position x that has unstretched length ?x as in Fig. 15.13. Ignoring the (small) curvature of the segment, its slope is Assume that the displacement of the string from equilibrium is small, so that has a magnitude much less than unity. Show that the stretched length of the segment is approximately (Hint: Use the relationship valid for |u|«1.) (d) The potential energy stored in the segment equals the work done by the string tension F (which acts along the string) to stretch the segment from its unstretched length ?x to the length calculated in part (c). Calculate this work and show that the potential energy per unit length of string is (e) Calculate are maximum where y is zero, and vice versa. (h) Show that the instantaneous power in the wave, given by Eq. (15.22), is equal to the total energy per unit length multiplied by the wave speed Explain why this result is reasonable.

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##### ISBN: 9780321675460

Since the solution to 85CP from 15 chapter was answered, more than 283 students have viewed the full step-by-step answer. This textbook survival guide was created for the textbook: University Physics, edition: 13. The answer to “CALC ?(a) Show that for a wave on a string, the kinetic energy per unit length of string is where is the mass per unit length. (b) Calculate for a sinusoidal wave given by Eq. (15.7). (c) There is also elastic potential energy in the string, associated with the work required to deform and stretch the string. Consider a short segment of string at position x that has unstretched length ?x as in Fig. 15.13. Ignoring the (small) curvature of the segment, its slope is Assume that the displacement of the string from equilibrium is small, so that has a magnitude much less than unity. Show that the stretched length of the segment is approximately (Hint: Use the relationship valid for |u|«1.) (d) The potential energy stored in the segment equals the work done by the string tension F (which acts along the string) to stretch the segment from its unstretched length ?x to the length calculated in part (c). Calculate this work and show that the potential energy per unit length of string is (e) Calculate are maximum where y is zero, and vice versa. (h) Show that the instantaneous power in the wave, given by Eq. (15.22), is equal to the total energy per unit length multiplied by the wave speed Explain why this result is reasonable.” is broken down into a number of easy to follow steps, and 219 words. The full step-by-step solution to problem: 85CP from chapter: 15 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. This full solution covers the following key subjects: string, length, segment, Energy, wave. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. University Physics was written by and is associated to the ISBN: 9780321675460.

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