Estimate the speed of sound (in m/s) in air a | vedclass

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(D) We know that $1$ mole of any gas occupies $22.4$ litres at $STP$. Therefore,the density of air at $STP$ is:$ho = \frac{	ext{mass of one mole of

Vedclass · Accepted Answer

$280$

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(D) We know that $1$ mole of any gas occupies $22.4$ litres at $STP$. Therefore,the density of air at $STP$ is:$ho = \frac{	ext{mass of one mole of air}}{	ext{volume of one mole of air at } STP}$$ho = \frac{29.0 	imes 10^{-3} \; kg}{22.4 	imes 10^{-3} \; m^3} = 1.29 \; kg/m^3$According to Newton's formula for the speed of sound in a medium,the speed of sound $v$ is given by $v = \sqrt{\frac{P}{ho}}$,where $P$ is the atmospheric pressure at $STP$ $(1.01 	imes 10^5 \; N/m^2)$.$v = \sqrt{\frac{1.01 	imes 10^5}{1.29}} \approx \sqrt{78294.57} \approx 280 \; m/s$.Thus,the estimated speed of sound is $280 \; m/s$.

Estimate the speed of sound (in $m/s$) in air at standard temperature and pressure $(STP)$. The mass of $1$ mole of air is $29.0 \times 10^{-3} \; kg$.

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