# Which material has the fastest speed of sound?

Sound travels faster in water than air. Sound travels faster in steel than air. But in which substance does it travel the fastest? Obviously there’s an upper limit of the speed of light, but would any material support near that? A neutron star? A Bose-Einstein condensate?

Something pretty dense would be a good guess. I read metallic hydrogen is supposed to conduct sound extremely well. It’s basically super compacted protons.

Wiki’s article has some math that is well beyond me for calculating the speed of sound. I’m sure someone will come along and blaze me.

I don’t know about metallic hydrogen, but beryllium at 42,200 feet per second is the fastest that I can find a cite for.

Something pretty stiff is a better guess.

Diamond is the stiffest commonly encountered material, but this stuff is stiffer still. I’ve no idea about the stiffness of the other states of matter Quartz mentions.

Trying to find a cite, but IIRC, as the mass of a neutron star increases, it’s materiel becomes ever denser and stiffer, which leads to an ever higher speed of sound. At 6 solar masses the speed of sound in a neutron star exceeds the speed of light, and therefore that’s one theoretical limit for how large they can be.

What you’ve quoted is referring to the speed of sound through a gas, not a solid.

As Struan says, something stiff is a better guess. More precisely, something “pretty dense” is not really a good guess at all. In general (from your Wikipedia link), the speed of sound is SQRT(C/[symbol]r[/symbol]), where C (or, for solids, E) is stiffness and [symbol]r[/symbol] is density. So high stiffness materials have a high speed of sound, and high density materials have a low speed of sound.

In a general, hand-waving sense, density and stiffness tend to scale with each other, which is why you might think as you did. Here’s a nice little graph of stiffness v. density for a number of common materials. The graph even includes some lines of constant [SQRT(E/[symbol]r[/symbol])], so you can see the highest results are beryllium and diamond (no surprise).

The speed of sound can reach c in a neutron star and you can’t go any faster than that.

Cool!

>the speed of sound in a neutron star exceeds the speed of light, and therefore that’s one theoretical limit for how large they can be

I was taught this, also, in ca. 1978. I understand it’s conventional wisdom in astrophysics.

Here’s the wiki on max size of neutron stars: http://en.wikipedia.org/wiki/Tolman-Oppenheimer-Volkoff_limit

I was going to ask a question here, but they covered it and I thougth somebody else might enojy the cite.

So what about black holes? Are they just a wild card?

I would guess the restriction that you can’t pass information “through” a black hole would somehow eliminate sound. Please stand by for someone who actually knows this stuff to show up.

Hmmm, I meant to say approach c not reach c. Neither sound, nor anything else, can reach or exceed c.

If an observer is stationary wrt to a black hole its event horizon appears to be a thermodynamic membrane. But if the observer is in free fall then it appears as nothing special at all. In addition, to a faraway stationary observer time comes to stop at the EH.

so given these conditions, I don’t see how you could even speculate as to what sound would do there. I know that I have no idea.

To the observer in free fall there’s nothing at the EH so there’s nothing to conduct the sound waves.

To the faraway stationary observer everything that ever fell into the BH is still at the EH but time comes to a stop so there also couldn’t be any sound waves.

However a guy named Finklestein developed a frame of reference that says even for the faraway stationary observer the infall still enters the hole in less than infinite time. But even if this is true that would just mean there’s again nothing to conduct the waves.

And finally there’s the close in stationary observer who sees a radiating thermodynamic membrane. It would seem for this guy that there would also be nothing there, so no sound waves.

So my guess is sound doesn’t propagate through the EH of the BH. Please take this as the Gospel truth until Chronos comes along and shows what a dolt I am.

Given that sound is just stuff banging into stuff, and that an event horizon marks the boundary of the volume around an object of sufficient mass that the escape velocity is greater than the limit c then it’s obvious that sound cannot escape.

This is probably a question based on a very naive view of black holes, but can sound enter the event horizon? I mean stuff goes into a black hole (I’m not even sure if that’s true if time slows down when approaching the horizon), but it can’t get out, right? IOW does the sound get stopped by the event horizon upon entry, by whatever is inside the horizon or by the horizon when reaching the other end of the black hole?

Sorry, when I say through the EH I don’t mean from outside the EH to inside, I mean within or along the surface of the curved spacetime that defines the EH.

Well as I said above; to the infalling observer time does not slow at the EH. So assuming material is falling into the hole I presume sound could also propagate into the hole.

However, for the faraway stationary observer, depending on how you interpret the Finklestein FoR, it could or it couldn’t.

Until Chronos tells me different I hold that it cannot, because time comes to a stop at the EH for this observer.

And yes nothing can pass through the EH from inside the hole. Although Hawking radiation, for all practical purposes, produces the same effects as particles escaping the hole.