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Q.
If the mass of $1 mol$ of air is $29.0 \times 10^{-3} kg$, then the speed of sound in air at standard temperature and pressure (using Newton's formula) is
Waves
Solution:
We know that, $1 mol$ of any gas occupies $22.4 L$ at standard temperature and pressure (STP), therefore density of air at STP is
$\rho_{0}= \frac{ { Mass of one mole of air }}{ { Volume of one mole of air at STP }} $
$=\frac{29.0 \times 10^{-3}}{22.4 \times 10^{-3}}=1.29 kg m ^{-3}$
Also, at STP, pressure of air is $1.01 \times 10^{5} Nm ^{-2}$.
So, according to Newton's formula for the speed of sound in medium, we get speed of sound in air at STP as
$v =\sqrt{\frac{p}{\rho_{0}}}=\left[\frac{1.01 \times 10^{5}}{1.29}\right]^{1 / 2}=279.81 ms ^{-1}$
$ \cong 280 ms ^{-1}$