Question

A copper rod of length 1.0 m is clamped at its middle point. Find the frequencies between 20 Hz and 20,000 Hz at which standing longitudinal waves can be set up the rod. The speed of sound in copper is $3.8km{s}^{-1}$.

Answer 1

Length of the wire =1.0 m

For fundamental frequency

$\frac{\lambda }{2}=I$

$\Rightarrow \lambda =2I=2\times 1=2m$

Here given n =3.8 km/s =3800 m/s

We know, $v=n\lambda$

$\Rightarrow n=\frac{3800}{2}=1.9kH$

So standing frequency between 20 Hz and 20 kHz which will be heard are

$=n\times 1.9kHz$

where n=0,1,2,3,....10.