Answer
3.68$\times$$10^{9}$ Hz
Work Step by Step
p = 1 atm = 101325 Pa
T = 0.00$^{\circ}$C = 273.15 K
d = 3.0$\times$$10^{-8}$cm = 3.0$\times$$10^{-10}$m
Speed of sound in the air $v_{sound}$ = 343 m/s
Boltzman constant k = 1.38 $\times 10^{-23}$
Using mean free path equation λ = $\frac{kT}{\sqrt 2 \times π \times d^{2}\times p}$
We calculated wavelenght of sound in air:
$λ_{sound}$ = 1.38$\times 10^{-23}$ $\times$ $\frac{273.15}{\sqrt 2\timesπ\times (3.0\times10^{-10})^{2}\times101325}$ = 9.3$\times10^{-8}$
Frequency of a wavelenght can be calculated by $f = \frac{v}{λ}$
$f_{sound}$ = $\frac{343}{9.3 \times 10^{-8}}$
$f_{sound}$ = 3.68$\times$$10^{9}$ Hz
