Question

According to Newton's formula, the speed of sound in air at STP is:
(Take the mass of $1$ mole of are is $29\times {10}^{-3}kg)$

• A. $250m{s}^{-1}$
• B. $260m{s}^{-1}$
• C. $270m{s}^{-1}$
• D. $280m{s}^{-1}$

Answer 1

The correct option is D $280m{s}^{-1}$

$1$ mole of any gas occupies $22.4$ liters at STP.
Therefore, the density of air at STP is
$\rho =\frac{\text{Mass of one mole of air}}{\text{Volume of one mole of air at STP}}$
$=\frac{29\times {10}^{-3}kg}{22.4\times {10}^{-3}{m}^3}=1.29kg{m}^{-3}$
At STP, $P=1atm=1.01\times {10}^{5}N{m}^{-2}$

$V=\sqrt{\left(\frac{P}{\rho }\right)}=\sqrt{\frac{1.01\times {10}^{5}N{m}^{-2}}{1.29\times kg{m}^{-3}}}=280m{s}^{-1}$