Speed of sound in a medium, no relation to given equation?

[chaser0]

---

Members do not see this ad.

We are given the formula to describe the speed of sound in a medium

v=(yP/density)^-1
= (yRT/M)^-1


The equation signifies that speed of sound is faster in less dense medium. But speed of sound is much faster in Iron and granite than it is in air.
I was wondering why this equation falls short.


Is there another equation I should refer to?

 

[chiddler]

can you please describe what the variables are?

 

[chaser0]

can you please describe what the variables are?

I notice you have BR. Check on page 6 of the physics II book.


I am basically wondering why:
If speed of sound is faster in a denser medium (faster in stone than in iron), why is it FASTER in LESS dense gases?

It's completely opposite of the solid and liquid mediums

 

[Buttafuoco]

If you have EK Audio Osmosis, they explain this. Basically the speed of sound decreases when the square root of density increases but it increases with the square root of bulk modulus. The density relates to its inertia which means the particles of a given medium are resistant to change from energy, but the bulk modulus relates to elasticity. Since things like iron and rock have very large bulk moduli, sound travels very fast through them. And that goes for pretty much any liquid or solid vs. any gas- consider that we can approximate any liquid or gas as incompressible for the MCAT whereas gases are highly compressible.

In short, solids are generally fast media for sound in spite of their density, not because of it.

 

[hellocubed]

haha, I was just looking at the same equation

http://imgur.com/UpkDZ


I was wondering. The equation also puts pressure to be directly related to velocity.
This seems to be somewhat of a double variable...

Increased pressure usually= increased density in gases

Is the density a fixed constant value in this equation? Or perhaps the increase in pressure has less effect on density than I am thinking?

 

[chiddler]

velocity of sound wave is proportional to bulk modulus and inversely proportional to density of the medium.

i've not yet had to use the formula and don't remember it exactly off the top of my head (pretty sure there's a square root somewhere), but this general relationship is accurate.

i don't know how to answer your specific question besides saying that as you go gas to liquid to solid, speed of sound increases but so does attenuation of intensity of sound.

edit: it's v=sqrt(Bulkmod/density). so the fastest velocity is a very inelastic and rigid medium.

 

[Buttafuoco]

haha, I was just looking at the same equation

http://imgur.com/UpkDZ


I was wondering. The equation also puts pressure to be directly related to velocity.
This seems to be somewhat of a double variable...

Increased pressure usually= increased density in gases

Is the density a fixed constant value in this equation? Or perhaps the increase in pressure has less effect on density than I am thinking?

I guess you can look at it certain ways to help clarify. Think about a mole of H2 and a mole Cl2 under the same conditions (and assume ideal behavior). They will have the same average KE per molecule and thus same pressure but it's much harder to get those bulky Cl2 molecules to move some way that those puny H2 molecules.

Remember that pressure is about gas particles moving around randomly with a certain amount of energy, whereas a sound wave is about directional movement. When you think about elastic collisions, you know that if you add energy to some molecules to displace them along some line, they are going to be colliding with randomly moving molecules in every direction back and forth. The more pressure (you could think of it as momentum density or something like that, the more probable that this translational motion is going to be transferred to another molecule in line quickly. Not to get all kaplany with a crappy metaphor, but think how much more quickly you could spread some gossip if you ran into a bored housewife every 10 steps as opposed to every 5 steps.

But, when you're transferring this momentum to the next molecule "in line," the same amount of momentum/energy results in a slower moving molecule for a molecule with more mass/inertia.