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 $9.00\times {10}^{-3}kg/m$ and is stretched to a tension of 20.0 N.

Answer 1

Fundamental frequency of the standing wave pattern formed on the string is given by $f=\frac{1}{2l}\sqrt{\frac{T}{\mu }}$

$=\frac{1}{2\times 30}\sqrt{\frac{20}{9\times {10}^{-3}}}=0.786Hz$

$n^{th}$ order harmonics are given by $\frac{n}{2l}\sqrt{\frac{T}{\mu }}$

Thus the respective harmonics are obtained for $n=2,3,4$

and are $1.57Hz,2.36Hz,3.14Hz$ respectively.