Question

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

Answer 1

For fundamental frequency, the relation between length and wavelength is:

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

So, wavelength of the wave:

$\lambda =2L=2\times 1=2m$

The speed of the wave is $3.8km/s$ or $3800m/s$.

The frequency of the wave is given as:

$f=\frac{v}{\lambda }$

$f=\frac{3800}{2}=1900Hz$ or $1.9kHz$

The value of the frequencies that can be heard in the range is :

$f^{\prime }=nf$ where $n=(1,2,3,4,.......10)$

For $n>10$, the frequency will become more than $20000Hz$.