Question

The range of the frequency of audible sound is 20 kHz. What is the range of wavelength for the audible sound at $0^{\circ }C$? (Take velocity of sound is 330$m{s}^{-1}$ at $0^{\circ }C$)

Answer 1

Hint: The speed (v) of the sound wave depends on the frequency (f) and wavelength ($\lambda$) of the sound wave as $v=f\lambda$. Substitute the given value of frequency and speed of sound at $0^{\circ }C$ in the equation and find the value of wavelength.

Complete step-by-step answer:
Sound is a wave produced due the vibrations of the molecules of air. When the molecules at a point are set into vibrations, these vibrating molecules set the surrounding molecules into vibrations. In this way a sound wave from a source propagates.
Since sound is wave, it will have some frequency and wavelength.
Frequency is the number of cycles completed in one unit time.
Wavelength is the distance that a wave travels in the time for which it completes one full cycle. Graphically, wavelength is the distance between any two consecutive troughs or crests of the wave.
The speed (v) of the wave depends on the frequency (f) and wavelength ($\lambda$) of the wave as $v=f\lambda$.
$\Rightarrow \lambda ={\displaystyle \frac{v}{f}}$
This is applicable to a sound wave too.
Human ear can only hear sound waves that have frequencies between 20Hz and 20kHz.
It is given that the range of the frequency of audible sound is 20 kHz. It is also given that speed of sound at $0^{\circ }C$ is 330$m{s}^{-1}$.
Therefore, the range of wavelength for the sound to be audible at $0^{\circ }C$ is $\lambda ={\displaystyle \frac{v}{f}}={\displaystyle \frac{330}{20\times {10}^3}}=16.5\times {10}^{-3}m=16.5mm$.

Note: Note that sound is longitudinal wave. It is formed due the continuous compressions and rarefaction of air. The vibrations of the molecules are along the direction of the propagation of these compressions and rarefactions or we can also say the propagation of the sound wave.