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 $360m{s}^{-1}$

Answer 1

The explanation for the answer is,

Speed of sound, $v=360m/sec$

Frequency for minimum wavelength, $f=20kHz$

Frequency for maximum wavelength,$f=20Hz$

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

$$\begin{gathered} v=f\lambda \\ \Rightarrow \lambda =\frac{v}{f} \end{gathered}$$

For minimum wavelength,

$$\begin{gathered} {\lambda }_{min}=\frac{360}{20\times {10}^3} \\ \Rightarrow {\lambda }_{min}=18x{10}^{-3}m \end{gathered}$$

For maximum wavelength,

$$\begin{gathered} {\lambda }_{max}=\frac{360}{20} \\ \Rightarrow {\lambda }_{max}=18m \end{gathered}$$

The minimum and maximum wavelength of sound are $18\times {10}^{-3}m.$ and $18m$ respectively.