The average range of frequencies at which human beings can hear sound waves varies from 20 Hz to 20 kHz. Calculate the wavelength of the sound wave in these limits. (Assume the speed of sound to be 340 m s-1.

The average range of frequencies at which human beings can hear sound waves varies from 20 Hz to 20 kHz. Calculate the wavelength of the sound wave in these limits. (Assume the speed of sound to be 340 m s-1.

Solution For a sound wave,

Speed = Wavelength x Frequency

ν = λ \times f
Given that the speed of sound in air = 340 m/s
\lambda_1=\frac{v}{f_1}=\frac{340}{20}=17m
\lambda_2=\frac{v}{f_2}=\frac{340}{20\times 10^3}=0.017m

Therefore, the audible wavelength region is from 0.017 m to 17 m when the velocity of sound in that region is 340 m s-1.