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Physics with MasteringPhysics | 4th Edition | ISBN: 9780321541635 | Authors: James S. Walker
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A steel guitar string has a tension T, length L, and

Chapter 14, Problem 105GP

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QUESTION:

Problem 105GP

A steel guitar string has a tension T, length L, and diameter D: Give the multiplicative factor by which the fundamental frequency of the string changes under the following conditions: (a) The tension in the suing is increased by a factor of 4. The diameter is D and the length is L. (b) The diameter of the string is increased by a factor of 3. The tension is T and the length is L. (c) The length of the string is halved. The tension is T and the diameter is D.

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QUESTION:

Problem 105GP

A steel guitar string has a tension T, length L, and diameter D: Give the multiplicative factor by which the fundamental frequency of the string changes under the following conditions: (a) The tension in the suing is increased by a factor of 4. The diameter is D and the length is L. (b) The diameter of the string is increased by a factor of 3. The tension is T and the length is L. (c) The length of the string is halved. The tension is T and the diameter is D.

ANSWER:

Step 1 of 4

(a) The frequency of the  harmonic for waves on a string is given by,

.............(1)

The speed of a wave on a string is,

..................(2)

where  is a mass per length, is,

Put the above value in equation two, implies,  

...................(3)

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