Question

A person can hear sound waves in the frequency range $20Hz$ to $20kHz$. Find the minimum and the maximum wavelengths of sound that is audible to the person. The speed of sound is $360m/s$.

Answer 1

The relation between wavelength $\lambda$ frequency $\nu$ and speed $v$ is given by:

$v=\nu \times \lambda$

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

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

For maximum wavelength $\nu =20Hz$.
as $(\nu \propto \frac{1}{\lambda })$

$\therefore {\lambda }_{max}=$ $\frac{v}{\nu }$ = $\frac{360}{20}$ =$18m$

For minimum wavelength, $\nu =20kHz$

$\Rightarrow {\lambda }_{mini}=$ $\frac{v}{\nu }$ = $\frac{360}{20\times {10}^3}$ = $18\times {10}^{-3}m$