Question

The human ear can detect continuous sounds in the frequency range from $20$Hz to $20,000$Hz. Assuming that the speed of sound in air is $330m{s}^{-1}$ for all frequencies, calculate the wavelengths corresponding to the given extreme frequencies of the audible range.

Answer 1

Speed of sound in air $v=330m/s$

Wavelength of sound wave $\lambda =\frac{v}{\nu }$

where $\nu$ is the frequency of sound wave.

Minimum frequency heard by human ear ${\nu }_{min}=20Hz$

So, maximum wavelength of sound wave ${\lambda }_{max}=\frac{v}{{\nu }_{min}}$

$\therefore$ ${\lambda }_{max}=\frac{330}{20}=16.5m$

Maximum frequency heard by human ear ${\nu }_{max}=20kHz=20000Hz$

So, minimum wavelength of sound wave ${\lambda }_{min}=\frac{v}{{\nu }_{max}}$

$\therefore$ ${\lambda }_{min}=\frac{330}{20000}=16.5\times {10}^{-3}m=16.5mm$