Question

If the mass of $1mol$ 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

• A. $250m{s}^{-1}$
• B. $280m{s}^{-1}$
• C. $300m{s}^{-1}$
• D. $380m{s}^{-1}$

Answer 1

Answer: (B)

We know that, $1mol$ of any gas occupies $22.4L$ at standard temperature and pressure (STP), therefore density of air at STP is
${\rho }_0=\frac{Massofonemoleofair}{VolumeofonemoleofairatSTP}$
$=\frac{29.0\times 10^{-3}}{22.4\times 10^{-3}}=1.29kg{m}^{-3}$
Also, at STP, pressure of air is $1.01\times 10^{5}N{m}^{-2}$.
So, according to Newton's formula for the speed of sound in medium, we get speed of sound in air at STP as
$v=\sqrt{\frac{p}{{\rho }_0}}={\left[\frac{1.01\times 10^5}{1.29}\right]}^{1/2}=279.81m{s}^{-1}$
$\cong 280m{s}^{-1}$