Answer to Question #226899 in Physics for Emyoung

Question

At what frequency would the wavelength of sound in air be equal to the mean free path of oxygen molecules at 1.0atm pressure and 0.00

Answer 1

The wavelength must be equal to the mean free path:

$$\lambda=l,\\\space\\ l=\frac{RT}{\sqrt2\pi d^2N_Ap}=\\\space\\ =\frac{8.314·273.15}{\sqrt2\pi (3·10^{-10})^26.022·10^{23}·1.01·10^5}=2.96·10^{-7}\text{ m}.$$

Assuming the speed of sound of 343 m/s, we have a frequency of

$$f=\frac{v}{\lambda}=\frac vl=\frac{343}{2.96·10^{-7}}=1.16·10^9\text{ Hz}.$$