How to create black holes with sound?

According to Sound Created Black Holes

First of all a sound of that magnitude would require $10^{98} W/m^2$ . That is an absolutely insane amount of power, far in excess of what we can produce, and is many of orders of magnitude greater than what a supernova creates. So we don’t have to worry about it actually happening. But, now, how would that create a black hole. By $E=mc^2$. Put enough energy into a small enough area and it would be the equivalent of putting mass in that area, causing immense gravity. With energy as great as 1100 $dB$, it would create enough gravity to cause a black hole to form, and an incredibly large one at that.

I expect a sound wave that strong would have to compress air so dense that the rest mass plus the kinetic energy would mean that the mass of say a metre cubed of air would fall inside it’s own Schwarzschild radius. When a mass of an object is compressed within it’s Schwarzschild radius, the escape velocity required to escape the sphere of matter the compression creates would exceed the speed of light, thus a black hole is formed.

An 1100dB sound wave would create a black hole. I guess this is because its pressure wave would compress the air to a smaller space than its Schwarzschild radius. But air and water are not solid, so how can I calculate a Schwarzschild radius for something that is not solid?

I guess the sound waves would make denser and less dense regions in the medium (air, water, plasma, etc...) and above a critical density this would create a black hole. I am not sure which equations I can use to calculate this density distribution made by the sound waves, and I cannot rearrange the equation of the Schwarzschild radius: $r_s = \frac{2GM}{c^2}$ to get something density related.

Can somebody write down the mathematical model of this example, or do I ask too much?

• I am more than likely misunderstanding you, but once you turn your sound system up to 11, do you not create from the air, (or water) an incredibly dense mass that can be treated like any other mass in these equations?The energy density itself mat be enough to create the singularity.Of course, how would you stop Newton's third law from applying, the "speakers" will need to be anchored somehow, and just be pedantic, and follow through of the logic/madness :) the mass required to stabilise them may be on the order of that necessary to create a BH. – user140606 Jan 21 '17 at 20:07
• Your comment to me: Not exactly the same equations. en.wikipedia.org/wiki/Schwarzschild_radius This text talks about compressing objects into a sphere, but in the experiment we are talking about sound waves. These waves would compress some regions of the space (air, water), so those regions would be denser, while other regions would be less dense. So I guess we should count something like a critical density. Hmm you are right it is possible to reorder this equation and use density instead of radius and mass. What equation can I use by sound waves to count the density space distribution – user140606 Jan 21 '17 at 20:09
• @Countto10 Let's forget about anchoring the speakers and that part of the problem and concentrate on the black hole and how the sound compresses the air. Is the energy density really enough to create a black hole? Can you give me a link about this? – inf3rno Jan 21 '17 at 20:11
• Your comment to me Nope I was wrong, in the equation we got $r_s=2GM/c^2r_s=2GM/c^2$, and to count critical density we need $ρ_crit=M/(4/3πr_s^3)$ – user140606 Jan 21 '17 at 20:12
• are you talking about sound in some kind of quark-gluon plasma? I do not think air can exist at those energy densities. – user126422 Jan 21 '17 at 23:51