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One string of a certain musical instrument is 75.0 cm long

University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman ISBN: 9780321675460 31

Solution for problem 46E Chapter 15

University Physics | 13th Edition

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University Physics | 13th Edition | ISBN: 9780321675460 | Authors: Hugh D. Young, Roger A. Freedman

University Physics | 13th Edition

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Problem 46E

One string of a certain musical instrument is 75.0 cm long and has a mass of 8.75 g. It is being played in a room where the speed of sound is 344 m/s. (a) To what tension must you adjust the string so that, when vibrating in its second overtone, it produces sound of wavelength 0.765 m? (Assume that the breaking stress of the wire is very large and isn’t exceeded.) (b) What frequency sound does this string produce in its fundamental mode of vibration?

Step-by-Step Solution:

Solution 46E Step 1: a) Equation for the frequency, f = v/ Where, v - speed of sound - Wavelength of the sound Provided, the speed of sound in air is, v = 344 m/s Wavelength of the 2nd overtone, = 0.765 m Therefore, frequency of the 2nd overtone, f = 344 m/s / 0.765 m f = 449.67 Hz Step 2: a) equation for the frequency of the sound is, 1 T f = 2L Where, L - length of the string T - Tension on the string - Linear mass density of the string = m/ L Square the equation, 2 1 T f = 4L2 Rearranging the equation to get tension on the string T = 4f L 2 Provided, mass of the string is, m = 8.75 g = 0.00875 kg Length of the string, L = 75 cm = 0.75 m Therefore, = m/L = 0.00875 kg / 0.75 m = 0.012 kg/m Substituting all these values in the above equation for tension we get, 2 2 T = 4 × (449.67 Hz) × (0.75m) × 0.012 kg/m 2 2 T = 4 × 202203 Hz × 0.5625m × 0.012 kg/m T = 5459.5 N Tension acting on the string would be, T = 5459.5 N

Step 3 of 3

Chapter 15, Problem 46E is Solved
Textbook: University Physics
Edition: 13
Author: Hugh D. Young, Roger A. Freedman
ISBN: 9780321675460

This textbook survival guide was created for the textbook: University Physics, edition: 13. The full step-by-step solution to problem: 46E from chapter: 15 was answered by , our top Physics solution expert on 05/06/17, 06:07PM. Since the solution to 46E from 15 chapter was answered, more than 1402 students have viewed the full step-by-step answer. This full solution covers the following key subjects: Sound, string, its, overtone, exceeded. This expansive textbook survival guide covers 26 chapters, and 2929 solutions. The answer to “One string of a certain musical instrument is 75.0 cm long and has a mass of 8.75 g. It is being played in a room where the speed of sound is 344 m/s. (a) To what tension must you adjust the string so that, when vibrating in its second overtone, it produces sound of wavelength 0.765 m? (Assume that the breaking stress of the wire is very large and isn’t exceeded.) (b) What frequency sound does this string produce in its fundamental mode of vibration?” is broken down into a number of easy to follow steps, and 85 words. University Physics was written by and is associated to the ISBN: 9780321675460.

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