Chapter 16, Problem 57CP

### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
ISBN: 9781337553278

Chapter
Section

### Physics for Scientists and Enginee...

10th Edition
Raymond A. Serway + 1 other
ISBN: 9781337553278
Textbook Problem

# A string on a musical instrument is held under tension T and extends from the point x = 0 to the point x = L. The string is overwound with wire in such a way that its mass per unit length μ(x) increases uniformly from μo at x = 0 to μL at x = L. (a) Find an expression for μ(x) as a function of x over the range 0 ≤ x ≤ L. (b) Find an expression for the time interval required for a transverse pulse to travel the length of the string.

(a)

To determine

The expression for μ(x) as a function of x over the range 0xL.

Explanation

The tension in the string is T and the extension point for string is 0 to L.

Assume the linear expression for the linear density Î¼(x) is,

Â Â Â Â Î¼(x)=ax+bÂ Â Â Â Â Â Â Â (1)

Here, Î¼(x) is the linear density at x.

Substitute 0 for x in equation (1).

Â Â Â Â Î¼0=aÃ—0+b=b

Substitute L for x in equation (1).

Â Â Â Â Î¼L=aL+bÂ Â Â Â Â Â Â Â (2)

Substitute Î¼(0) for b in equation (2)

(b)

To determine

The expression for the time interval required for transverse pulse to travel the length of the string.

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