# In what ways do high altitudes affect speed of sound?

1. Mar 29, 2015

### Clueless

This is what I am pondering about: At high altitudes, it makes sense that lower temperatures will correspond with velocity of sound travelling through the air at higher altitudes. With lower temperatures the movement of the gas molecules will slow down, making it more difficult for sound to travel through this medium (I am aware that I might be too general in my explanation).

But a formula I came across - $c_s = \sqrt (\frac{\gamma*k*T} {m})$ - where $\gamma$ is the adiabatic exponent, $k$ Boltzmann's constant, $T$ the temperature, and $m$ the mass, seems to indicate to me that there is another variable, $m$ to consider.

So how could mass of the air affect sound's velocity as it passes through? I don't know. I suppose the mass of the air correspond with the number of air molecules as well as what the air is made up with. Does increasing the number of air molecules decrease the speed of sound? If so, how? Do more particles make it more difficult for energy to travel? If so, why?

PS I apologize if I am asking way too many questions...please tell me so if this is the case!

2. Mar 29, 2015

### Staff: Mentor

In your equation, m is the mass of a gas molecule. You could have found that out by looking up "speed of sound" on Wiki. It took me less time to do that than it did for you to write out your question.

Chet

3. Mar 29, 2015

### Clueless

My goodness...that was a daft thing to do on my part Made things much clearer but I would like to clarify...

So increasing the mass of gas molecules will decrease the velocity of sound because heavier particles (intuitively and by Newtonian mechanics) would need have the same velocity as lighter particles if both are given the same energy?

4. Mar 29, 2015

### Staff: Mentor

I have no idea what this means. More massive molecules have more inertia than less massive molecules, and require more force to accelerate.

Chet