Question

Question 7
A person has a hearing range from 20 Hz to 20 kHz. What are the typical wavelengths of sound waves in air corresponding to these two frequencies? Take the speed of sound in air as $344m{s}^{-1}$.

Answer 1

For a sound wave,
Speed = Wavelength $\times$ Frequency
$V=\lambda \times f$
Speed of sound in air = 344 m/s (Given)

(i) For, f = 20 Hz
${\lambda }_1=\frac{V}{f}=\frac{344}{20}=17.2m$

(ii) For, f = 20000 Hz
${\lambda }_2=\frac{V}{f}=\frac{344}{20000}=0.0172m$

Hence, for humans, the wavelength range for hearing is 0.0172 m to 17.2 m.