Sound’s speed is directly proportional to the density of its medium. e.g. it’s faster underwater than in the air.
So…
If the medium were super dense, such as a black hole, could sound attain near light speed?
Godd question! I’m trying to picture putting my ear against the surface of a black hole (ignoring the fact that this is obviously impossible…) and whanging the BH hard with a baseball bat…
Seems to me that as density increases, there would have to be a point at which the molecular vibration, which allows for transmission of sound, would break down… IE: if the matter were dense enough, there would be no possibilty of sound tranmission. Then again, I currently have my head up a black hole, as it were… 
Or, maybe at the highest possible density, the entire mass would behave as a single particle, and sound transmission would be instantaneous?? Oh crap… it’s been a LONG day!!!
Someone? Please help!! My head hurts!
Well, yes, although this is extrapolating the laws of physics we know about into a zone where they may no longer apply. We can’t know anything about what happens on the other side of an event horizon - the common concept of a point of infinite density is impossible to prove.
I’d imagine the speed of sound in neutronium is pretty damned fast though!
This one got me thinking…
Minor note, the speed of sound is given by sqrt(B/r) where Bulk modulus of the medium and r is density. You are quite correct the speed of sound is higher in water than air (SoS air (0 deg C): 331m/s, Water: 1402m/s), but this is due to the higher Bulk Mod. of water, not it’s higher density (a higher desnisty actually decreases the speed of sound).
As for your question: I haven’t a clue :). My guess is there are some weird stuff that happens when density gets real low or real high. No idea what a black hole sounds like.
Spent most of the night thinking about this one; here’s my (pretty good sounding, if I do say so myself) WAG:
A black hole is by definition perfectly incompressible consequently, sound is impossible.
A perfect vacuum is infinitely compressible, but the intensity of the sound in a vacuum is zero.
Put any chunk of matter (one atom for example) in it, and the limiting factor for the speed of sound (to my way of thinking, at least) is the original speed of the matter plus the energy of the sound entirely as speed of the particle. I don’t see why this could not approach the speed of light, but in these terms begs the question whether this could still be considered sound.
My WAG:
Doesn’t the speed of sound rise with the rigidity of the material? Thus sound travels faster in steel than air? It also makes sense that the speed would drop with increasing density (harder to wiggle those heavy substances).
So the “fastest” material material for sound would be very rigid but very light. I suspect that rigidity overpowers density, so to speak, as both rise, and a dense but rigid substance would still conduct sound quickly.
If neutron stars are rigid masses of neutrons packed side-by-side, they may conduct sound at great speed.
But I don’t see how a black hole would have enough extent to conduct sound: a black hole is just an indefinitely massive point, the singularity. We may speak of the radius of a black hole, but that is really the radius of the event horizon, the location beyond which it is no longer possible to escape the hole. There is no actual physical surface on a black hole. (I’m ignoring issues of spin and electrical charge on the hole. Add those, and things get weird.)
If you want to achieve near-light-speed speed-of-sound, increase the temperature. As the temperature of a gas increases, the speed of sound increases because the indivudual particles are moving faster. Increase the temperature high enough, and the particles will be moving near-light speed. I’d expect that the speed-of-sound will then also approach the speed-of-light.
This works for solids and liquids as well, because when the temperature is high enough, they’ll turn into gasses, too.
Many think in black hole matter is in-compressible so sound couldn’t travel but i got to black hole matter is compressible and it is given
v^2 = 0.9 x c^2
in case of rotating black holes
but generally v is bounded below c / (sqrt2)
if you want more details see this link
http://www.dias.ie/images/stories/theo/preprints/DIAS-STP-11-11/DIAS-STP-11-11.pdf
I remember having to calculate this in my freshman astrophysics course. IIRC, if you calculate the density at which the sound of speed is equal to c, that turns out to correspond to the upper limit of mass (i.e. upper limit of density) for neutron stars.
A black hole doesn’t have a defined size (or it has a size of zero), so sound speed is undefined. (The event horizon has a size, but that’s not a physical, solid object.)
If that’s the case then my vote is for aerogel.
It’s true. If you crash a meteor into a neutron star, someone the other side will see the flash the exact same instant they hear a faint ringing sound … “B.r.r.r.r.r.r.r.a.a.a.i.i.i.i.n.n.n.n.s.s.s.s.s”…