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?
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[Physics] Speed of sound in hydrogen vs. speed of sound in air
acousticsairdensityspeed
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A sound wave is not particles oscillating, is a mechanical oscillation of a medium made of particles. It is important to separate the medium behaviour from the particle behaviour. Medium behaviour results from the averaging over the values of the many particles, and this generates essentially different phenomena.
A way of visualizing it is thinking of a demonstration or a public gathering: although many people are moving through, trying to reach a friend or coming out or in, the bulk behaviour is what matters if you would see from a plane. From above the mass would look static, even if below there is almost nobody standing in one place. The same is with movement, although not every person might move in the direction of the bulk, from above a marching crowd would look so. But the speeds and directions might differ very much.
So when sound travels through a medium, average densities oscillate due to pressure increase and vice versa. But local densities at a microscopic scale might me much larger than the bulk ones, because even if two particles can come very close, many of them cannot be so close together due to the much higher potential energy related.
So your analogy cannot be followed for these reasons, and this is also the cause that we use different formulations to describe groups of 10 or 100 particles, than when we describe media (made of at least ~$10^{23}$).
To first order, the speed of sound is not affected by pressure. Pressure waves can be shown to fulfill the D'Alembert wave equation $(c_S^2\,\nabla^2 - \partial_t^2)\psi=0$ where the wavespeed $c_S$ is given by:
$$c_S = \sqrt{\frac{K}{\rho}}$$
where $K$ is the bulk modulus of the medium in question and $\rho$ its density. Now, for an ideal gas, the bulk modulus $K$ is in most conditions proportional to the pressure; if the compression is adiabatic (good approximation for high frequency sound, as there is little time for heat to shuttle back and forth in the gas), then $K=\gamma\,P$, where $\gamma$ is the Heat Capacity Ratio or Adiabatic Index. However, from the ideal gas law $P\,V=n\,R\,T$ we have:
$$\rho = \frac{n\,M}{V} = \frac{P\,M}{R\,T}$$
where $M$ is the mean molar mass of the gas in question in kilograms. Thus the pressures cancel out in the speed of sound:
$$c_S = \sqrt{\frac{\gamma\,R\,T}{M}}$$
Thus we see that the speed is also weakly affected by the humidity - more water in the air lowers the mean molecular mass. If we put $M=0.029$, $T=300K$ and $\gamma = 1.4$ for air, we get $c_S=347{\rm m\,s^{-1}}$.
Best Answer
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.