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 in the rod. The speed of sound in copper is $3.8km{s}^{-1}$

• A. $n\times 1.9kHz$ $n=1,2,\mathrm{3.....}10$
• B. $n\times 3.1kHz$ $n=1,2,3,4,5,6$
• C. $n\times 5kHz$ $n=1,2,3,4$
• D. None of these

Answer 1

The correct option is A

$n\times 1.9kHz$

$n=1,2,\mathrm{3.....}10$

Length of wire = 1.0 m

For fundamental frequency $\frac{\lambda }{2}=l$

$\Rightarrow \lambda =2l=2\times L=2m$

Here given v = $3.8km{s}^{-1}$= $3800\frac{m}{s}$

We know $\Rightarrow v=f\lambda \Rightarrow f=\frac{3800}{2}=1.9kHz$.

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

$f=$ $n\times 1.9kHz$
where n = 1, 2, 3,..... 9, 10