Question

A sonometer wire having a length of 1.50 m between the bridges vibrates in its second harmonic in resonance with a tuning fork of frequency 256 Hz. What is the speed of the transverse wave on the wire ?

Answer 1

First harmonic be $f_0.$

Second harmonic be $f_1$.

$\Rightarrow f_1=2f_0$

$f_1=256Hz$

$\therefore 1^{st}$ harmonic or fundamental frequency

$f_0=\frac{f_1}{2}=\frac{256}{2}=128Hz$

$\frac{\lambda }{2}=1.5m$

$\Rightarrow \lambda =3m$

[When fundamental wave is produced]

$\Rightarrow$ Wave speed = V

$=f_0\lambda =128\times 3=384m/s$