# Density and Speed of Sound

Q:
Just a question about Physics I'm doing at school.If the speed of sound is inversely proportional to the density of a material, why does sound travel faster in solids (it is the most dense).I have read that it takes more energy for sound to travel in dense materials so it takes longer but then neighbouring molecules are closer so sound does not have to travel that far, making it faster. This doesn't make any sense because it says the more dense a medium is, sound is both faster and slower.Also, how does bulk modulus affect the speed of sound.
- Abhishek (age 15)
Australia
A:

It's true that the, other things being equal, the speed of sound goes down as the mass density goes up. The problem is that other things usually aren't equal. A little ripple in the density of a piece of steel creates much bigger forces than a similar percentage ripple in the density of some air. So those bigger forces speed up the sound. Another way of saying that is that the sound speed goes up for bigger bulk modulus. (That's the compressive longitudinal sound. Transverse sound depends on the shear modulus.) For ideal gases, the two factors just cancel and the speed of sound doesn't depend on the density. In typical solids the bulk modulus goes up by a bigger factor than the density does, compared to gases, so solids typically have faster sound waves.

Mike W.

(published on 10/24/2015)

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