College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 11 - Problems - Page 431: 59


The fundamental frequency increases by 7.0%

Work Step by Step

We can write an expression for the wave speed along a string: $v = \sqrt{\frac{F}{m/L}} = \sqrt{\frac{F~L}{m}}$ We can find an expression for the fundamental frequency: $f = \frac{v}{\lambda}$ $f = \frac{\sqrt{\frac{F~L}{m}}}{2L}$ $f = \frac{1}{2}~\sqrt{\frac{F}{m~L}}$ We can find the new fundamental frequency when the tension increases by 15%: $f' = \frac{1}{2}~\sqrt{\frac{1.15~F}{m~L}}$ $f' = \sqrt{1.15}\times\frac{1}{2}~\sqrt{\frac{F}{m~L}}$ $f' = \sqrt{1.15}\times f$ $f' = 1.07\times f$ The fundamental frequency increases by 7.0%
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