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:
$\lambda= \frac{v}{f}$
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
$\lambda_1 = \frac{v}{f_1}= \frac{344 m/s}{20.0 Hz}=17.2 m$
The highest frequency is $f_2 = 2.00 \cdot 10^4 Hz$, so the corresponding wavelength is
$\lambda_2 = \frac{v}{f_2}= \frac{344 m/s}{2.00 \cdot 10^4 Hz}=0.017 m$

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