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 344 ms^-1.

Given,

Speed (v_air) = 344 ms^-1

We know,

Speed (v) = Wavelength (λ) x Frequency (ν)

or

Wavelength (λ) = $\dfrac{\text{v}}{\text{ν}}$

(a) For ν = 20 Hz, substituting we get,

λ₁ = $\dfrac{344}{20}$ = 17.2 m

(b) For ν = 20,000 Hz, substituting we get,

λ₂ = $\dfrac{344}{20,000}$ = 0.0172 m

Hence, typical wavelengths of sound waves in air corresponding to 20 Hz and 20,000 Hz are 17.2 m and 0.0172 m respectively.