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 3.8 km s−1.

Answer 1

Explanation:

Step 1:

The rod shall act as an open organ pipe for the longitudinal sound waves. The levels for the longitudinal waves on stand will be $v=n V / 2 L$

$v=n \times \frac{3800}{(2 * 1.0)} H z$, where $n=1,2,3, \ldots$ { Despite the speed of copper's tone,$\mathrm{V}=3.8 \mathrm{km} / \mathrm{s}=3800 \mathrm{m} / \mathrm{s}$}  

$v=1900 n \mathrm{Hz}$

Step 2:

So the minimum frequency for $\mathrm{n}=1, \text { is i.e. }=1900 \mathrm{Hz}$

Maximum frequency is for $n=10, \text { i.e. }=19000 \mathrm{Hz}=19 \mathrm{kHz}$  

The $n=11$ value will give a frequency of $=20.9 \mathrm{kHz}$ which is more than $20000 \mathrm{Hz}$

The standing longitudinal wave frequencies are therefore $v=1.9 n \mathrm{kHz}$ where $n=1,2,3,4, \ldots, 10$