Question

The range of audible frequencies is from about 20.0 hz to 2.00×104 hz . what is range of the wavelengths of audible sound in air? the speed of sound in air is 344 m/s.

Answer 1

The wavelength is related to the frequency by the relationship:

`\lambda= (v)/(f)`
where v is the wave speed and f is its frequency.

The speed of sound in air is v=344 m/s. The lowest frequency is f=20.0 Hz, so the corresponding wavelength is

`\lambda_1 = (v)/(f_1)= (344 m/s)/(20.0 Hz)=17.2 m`
The highest frequency is
`f_2 = 2.00 \cdot 10^4 Hz`, so the corresponding wavelength is

`\lambda_2 = (v)/(f_2)= (344 m/s)/(2.00 \cdot 10^4 Hz)=0.017 m`

Therefore, the range of wavelengths of audible sound in air is
[0.017 m - 17.2 m]