Question

A transverse wave is produced on a stretched string $0.9$m long and fixed at its ends. Find the speed of the transverse wave, when the string vibrates while emitting second overtone of frequency $324$Hz.

Answer 1

Length of the string $L=0.9$ m

For second overtone frequency (or third harmonic mode of vibration) $n=3$

Frequency of nth mode of vibration when the string is fixed at both ends $\nu =\frac{nv}{2L}$

$\therefore$ $324=\frac{3v}{2\left(0.9\right)}$

$⟹$ $v=\frac{324\times 0.9\times 2}{3}=194.4$ $m/s$

We get speed of transverse wave, $v=194.4$ $m/s$