# Are 'sound speed' and 'speed of sound' the same thing?

If not, what is the difference?

If they are, could you clarify how the speed of sound applies in the below description of gaseous clouds?

Background

I recall taking an astronomy class several years ago where the instructor said that the sound speed of gaseous clouds affected whether or not they collapsed and star formation began. This is of course a simplification, but this was my basic understanding:

As clouds become more massive, they contract due to the force of gravity. As they contract, they heat up. This heat causes expansion, which counteracts the force of gravity and prevents collapse.

As I recall (correct me if I'm wrong. I'm probably over simplifying at the very least), if sufficient mass is added, or if the sound speed is too small, then the cloud collapses faster than it can heat up and counteract the collapse. In my mind, the cloud is collapsing faster than the information is traveling through the cloud telling it that it should be heating up.

research

Searching 'sound speed' returns a lot of results about the speed of sound. This leads me to think they are the same, but this goes against what I remember.

There are also a couple results for sound speed on this SE, but they are incomprehensible to me.

• I use them interchangeably – Kyle Kanos Nov 15 '15 at 12:12
• Maybe I'll have to find that professor and email him then to figure out exactly what was going on. Thank you. – Liam Nov 15 '15 at 12:14
• I wrote a detailed answer to another question about the speed of sound at: http://physics.stackexchange.com/a/179057/59023. – honeste_vivere Nov 15 '15 at 14:20

Now in an ideal gas, sound speed and temperature are linked via $$c^2_{\rm s} = \frac{k_B T}{\mu}$$. It is thus equivalent to say that the temperature is too small and the cloud collapses because of that, or to say that the sound speed is not large enough to stabilize the cloud in time against its own gravity. Maybe that's where the confusion is coming from.