# Speed of Sound

#### Sidious

##### Well-Known Member
I'm interested to know why the speed of sound is directly related to air temperature. I have the mistaken impression that it is related to air density, which, from what I've read is incorrect. I'm confused on the term stiffness and how that it is the real culprit for the change in speed.

Any info, links, or sources would be great!

Thanks

#### tgrayson

##### New Member
I'm interested to know why the speed of sound is directly related to air temperature.

Molecules bounce around because they're hot, or rather, temperature is determined by how much the molecules bounce around. The greater the average velocity, the hotter the temperature.

When you increase the energy of a molecule by emitting a sound, it will carry that extra energy to other molecules as it bounces from one to another. It can only carry that energy to another molecule at the speed it's moving in the same way giving a letter to the postman will only get to the office as fast as he's driving. And that's only if he takes the direct route, which he won't.

So temperature is a mere stand-in for the average molecular velocity.

Density and pressure do affect the speed of sound in solids, but don't in gases, because an increase in pressure results in decrease in density, so they cancel out.

#### Sidious

##### Well-Known Member
Density and pressure do affect the speed of sound in solids, but don't in gases, because an increase in pressure results in decrease in density, so they cancel out.

Followed everything except that last part.... Pressurizing air makes it more dense no? The reason I say that is in dealing with engine performance as we go to altitude and the pressure is reduced the air is less dense thus depleting that performance.

#### tgrayson

##### New Member
Followed everything except that last part.... Pressurizing air makes it more dense no?

Yes, but the formula for speed of sound divides pressure by density, so they increase or decrease at the same rate, which eliminates their effect. (for gases) This makes everything else in the equation a constant, except for temperature.

(Ok, I see where that question came from....I mistyped in my original post. The increase/decrease should be increase/increase.)

#### Realms09

##### Well-Known Member
The ideal gas equation of state excludes molecular interactions (van der Waals forces, etc.). Similarly, inviscid flow also excludes molecular iteractions by ignoring viscosity and thermal conductivity. Therefore, a derivation that uses the ideal gas EOS and inviscid flow assumptions should not give a result dependent on the number of molecules in a given space because in this framework the molecules never collide. And as the math turns out, density does in fact go away.

Thanks!

#### Realms09

##### Well-Known Member
Sidious, it's been awhile but there was a line of thought I wanted you to explore. The speed of sound is the speed at which a pressure disturbance propogates, and tgrayson explained in air it can only go as fast as the molecules themselves are going, which is measured by temperature.

How is it, then, that the speed of sound depends on density in a solid? Why isn't it also just directly related to temperature?