A sample of oxygen at NTP has volume $V$ and a sample of hydrogen at NTP has volume $4 V$ . Both the gases are mixed and the mixture is maintained at NTP, if the speed of sound in hydrogen at NTP is $1270 m s^{- 1}$ , then calculate the speed of sound in mixture.

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Solution

Speed of sound $\propto \frac{\sqrt{P r e s s u r e}}{\sqrt{d e n s i t y o f g a s}}$
given at NTP so, $P$ is constant
$∴ S \times \sqrt{d e n s i t y}$ is constant
$1270 \times \sqrt{1} = x \times \sqrt{\frac{4 \times v + 16 \times v}{5 v}}$
$= x \times 2$
$\Rightarrow x = 635 m / s$ .

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