# Shockwaves speed through rarer and denser atmosphere

I was going through the different speed of sound through different atmospheric/air conditions and the Newton-Laplace equation gives

$c=\sqrt{\frac{\gamma P}{\rho}}$

So, where does the temperature come into effect for the air here? So, does the sound wave travel equally fast through the same gas maintained at different temperatures but same pressure?

Also, does the shockwave replicate these properties i.e.,

i) Does the shockwave travel faster through the denser atmosphere or rarer atmosphere maintained at same temperature and pressure?

ii) How does the speed of the shockwave vary with change in temperature/ pressure/ density of the air?

• By the ideal gas law, masses of air at the same pressure but different temperatures have different densities, so the sound speed is still different. – probably_someone Nov 26 '17 at 20:21
• But what if temperature and pressure is maintained the same and volume expansion causes density to change for given moles of a gas/air? And what about the answer to the shockwaves question? – Your IDE Nov 27 '17 at 10:29
• How do you maintain a constant temperature and pressure while increasing the density? The speed of sound is actually defined as $$C_{s} = \frac{\partial P}{\partial \rho}$$ and only reduces to the equation you show after one assumes an adiabatic equation of state. – honeste_vivere Nov 27 '17 at 14:04