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Question

Find the fundamental frequency and the next three frequencies that could cause a standing-wave pattern on a string that is 30.0 m long, has a mass per unit length of 9.00×103kg/m and is stretched to a tension of 20.0 N.

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Solution

Fundamental frequency of the standing wave pattern formed on the string is given by f=12lTμ
=12×30209×103=0.786Hz
nth order harmonics are given by n2lTμ
Thus the respective harmonics are obtained for n=2,3,4
and are 1.57Hz,2.36Hz,3.14Hz respectively.

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