A person has a hearing range from 20 Hz to 20 KHz. What is the typical wavelength of sound waves in air corresponding to these frequencies ? Take the speed of sound in air as `344 ms^ -1`.

Explanation

Case I: Frequency, v= 20Hz, Speed of sound in air, V= `344m s^(-1)`, Wavelength, `lamda`= ?
Speed = Wavelength `xx` Frequency
`rArr V= lamda xx v`
`rArr 344 ms^(-1) = lamda xx 20Hz`
`rArr lamda= (244 ms^(-1))/(20Hz)= 17.2m`
Case II: Frequency, v= 20 kHz= 20,000Hz
Speed of sound in air, `V= 344 ms^(-1)`
Wavelength, `lamda`= ?
Speed = Wavelength `xx` Frequency
`rArr V= lamda xx v`
`rArr 344 ms^(-1)= lamda xx 20,000Hz`
`rArr lamda= (344 ms^(-1))/(20,000Hz)= 0.0172m`
Thus, the wavelength of sound corresponding to 20 Hz and 20 kHz is 17.2m and 0.0172 m respectively.