How much faster does sound travel in hydrogen with density 0.0896 g/L than in air with density 1.293 g/L at the same temperature and pressure?
- Is there any solution to solve this?
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$\begingroup$ see also en.wikipedia.org/wiki/Speed_of_sound - apparently this will also depend on the type of hydrogen. Also, density is not really all that counts... $\endgroup$– MartinCommented Jul 15, 2015 at 13:14
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2 Answers
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The speed of sound in an ideal gas is given by:
$$ v = \sqrt{\gamma\frac{P}{\rho}} $$
where $P$ is the pressure, $\rho$ is the density and $\gamma$ is the heat capacity ratio. For ideal diatomic gases $\gamma = 1.4$. In fact for air at 20ºC $\gamma$ is almost exactly 1.4, while for hydrogen it's 1.41, so pretty close to ideal behaviour.
answered Jul 15, 2015 at 17:02
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Another way to view the same relationship which @JohnRennie gave is $$v=\sqrt{\gamma\frac{RT}{M}},$$ where $R$ is the ideal gas constant, $T$ is the absolute temperature, and $M$ is the molecular mass of the gas. $\gamma$ is the heat capacity ratio, as mentioned in his answer.
Since you were directly given the densities, his form works more directly, but this helps see what happens if the temperature changes. The molecular mass of gaseous hydrogen will be 2.0 grams per mole and of air will be 28.8 grams per mole. (Be sure to use appropriate units if you need to calculate an actual value of $v$.)
