# Speed of a Wave vs. Density of a Medium

1. Dec 13, 2015

### jumbogala

1. The problem statement, all variables and given/known data
Hi everyone. I watched a YouTube video earlier today which said that sound waves travel faster in more dense mediums. For example, sound travels faster in water than it does in air.

However, on this webpage http://www.physicsclassroom.com/mmedia/waves/ltm.cfm it says that "the wave speed is always greatest in the least dense medium".

So which is true?
2. Relevant equations

3. The attempt at a solution
I am thinking that maybe it depends on the type of wave, and that transmitted/reflected waves work differently than sound waves.

2. Dec 13, 2015

### haruspex

As I understand it (not an expert though) it depends what you mean by going to a denser medium.
Increasing the mass of the individual particles (gas molecules, atoms in a solid lattice..) will reduce the speed.
Packing the particles closer or increasing their repulsion may increase the speed.
For an ideal gas, the speed is $\sqrt{\frac{\gamma p}{\rho}}$, where p is pressure and rho is density, so increasing pressure but holding temperature constant should not make any difference. The higher pressure balances the increased density.
For a fluid in general it is $\sqrt{\frac{K}{\rho}}$, where K is the bulk modulus. For the gas case, that reduces to the same as above, but liquids have a much higher bulk modulus than gases (more than the relative increase in density), so going from gas to liquid tends to increase the speed.
The speed of sound in water reaches a maximum at about 70C, then declines a little.

3. Dec 14, 2015

### lychette

In a gas the speed of sound depends on the mass of the molecules (∝√1/m)) and on the absolute temperature (∝√T) so for any particular gas the only major effect is Temperature. Sound is transmitted by translational movement of molecules. (density has little influence)
In liquids and solids sound is transmitted by vibrational motion of molecules and the elastic properties of the solid or liquid are the major influence on the speed.
Light, of course, does slow down as it passes into the more dense medium and a phase change occurs in any reflection from less dense to more dense medium. This is noted in the 'physics classroom' site that you mentioned.

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