Speed of Sound

[shefv]

I am confused about this

I know that speed of sound is fastest in solid, then liquid and slowest in gas

but when looking at the relationship with density - it is faster in a substance with lower density

I have always thought that solids have a greater density than air so the two facts don't seem to line up in my mind.

Can someone please explain?

Thanks!

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[NextStepTutor_3]

This is a great question! Both of your facts are absolutely true. Sound is fastest in solids, then liquids, and slowest in gases; all else being equal, sound is also faster in substances that are less dense. If we consider density alone, these two facts seem to contradict each other, causing tons of confusion.

Here's why it works out. The equation that you'll most commonly see is this one:

...where v is the speed of sound, B is the bulk modulus, and rho is density. Notice that both density and the bulk modulus matter! Specifically, the higher the bulk modulus, the faster sound will travel. I like to think of bulk modulus as a measurement of how hard it is to compress something. Solids, then, will have a high bulk moduli (you can't easily compress them) while gases, for example, will have extremely low bulk moduli.

So, even though solids are more dense than gases (which would tend to decrease the speed of sound), they also have a higher value for B, which tends to have a larger effect, making the speed increase overall. When, then, does density matter? Imagine that you're comparing two solids with similar bulk moduli. In this case, the solid with the higher density will be the one through which sound travels slower.

 

[NextStepTutor_3]

Just a quick addendum on why bulk modulus matters so much:

Sound waves are longitudinal, unlike light waves. This means that, instead of "cutting through" the medium perpendicularly, they displace the medium in the same direction as they propagate. In other words, sound waves travel by making areas of compression and rarefaction (un-compression) in the medium. This explains why sound doesn't travel in a vacuum - there's no medium to compress at all.

This actually confused me for a while. If sound operates by compressing matter, why doesn't it move faster in gases? After all, gases are easy to compress. The answer lies in their elasticity, or ability to "bounce back" to their original state. When a sound wave compresses a gas, it takes longer for that gas to "un-compress," or rarefact. This slows down the wave. A solid, on the other hand, is more "springy" - it likes to retain its original shape. Because of this, sound waves can propagate quickly through solids.