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

Given:
Length of copper rod l = 1.0 m
Speed of sound in copper v = 3.8 kms⁻¹ = 3800 m/s
Let f be the frequency of the longitudinal waves.

Wavelength $\left(\lambda \right)$ will be:
$$\begin{gathered} \frac{\lambda }{2}=I \\ \Rightarrow \mathrm{\lambda }=2I=2\times 1=2\mathrm{m} \end{gathered}$$

We know that:
v = fλ
$\Rightarrow f=\frac{v}{\lambda }$
So,
$f=\frac{3800}{2}=1.9\mathrm{KHz}$
Therefore, the frequencies between 20 Hz and 20 kHz that will be heard are
= n × 1.9 kHz,
where n = 0, 1, 2, 3, ...10.