Answer to Question #226899 in Physics for Emyoung

Question #226899
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
1
Expert's answer
2021-08-18T02:25:02-0400

The wavelength must be equal to the mean free path:


λ=l, l=RT2πd2NAp= =8.314273.152π(31010)26.02210231.01105=2.96107 m.\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=vλ=vl=3432.96107=1.16109 Hz.f=\frac{v}{\lambda}=\frac vl=\frac{343}{2.96·10^{-7}}=1.16·10^9\text{ Hz}.


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