Question

The range of human hearing extends from approximately 20 Hz to 20 000 Hz. Find the wavelengths of these extremes when the speed of sound in air is equal to 338 m/s. The smallest wavelength that can be heard is: Incorrect: Your answer is incorrect. m The longest wavelength that can be heard is: m

Answer 1

Explanation:

Given that,

The range of human hearing extends from approximately 20 Hz to 20 000 Hz. We need to find the wavelengths of these extremes when the speed of sound in air is equal to 338 m/s.

Speed of any wave is given by :

$v=f\lambda$

$\lambda$ is wavelength of wave

If f = 20 Hz

$\lambda=\dfrac{v}{f}\\\\\lambda=\dfrac{338}{20}\\\\\lambda=16.9\ m$

If f = 20000 Hz

$\lambda'=\dfrac{v}{f'}\\\\\lambda'=\dfrac{338}{20000}\\\\\lambda'=0.0169\ m$

The smallest wavelength that can be heard is 0.0169 m and the longest wavelength that can be heard is 16.9 m.