# B Can sound distort the fabric of space?

1. Apr 21, 2017

### John Clement Husain

Is it possible for Low Frequency to distort the fabric of space? If so, how?

2. Apr 21, 2017

### Staff: Mentor

Low Frequency what?

3. Apr 21, 2017

### John Clement Husain

of Sound

4. Apr 21, 2017

### Staff: Mentor

Sound requires a medium, such as air. The medium will have nonzero stress-energy, so it will curve spacetime, yes. The sound itself will contain some energy, but that will be included in the stress-energy tensor of the medium if we properly evaluate that tensor with the sound present.

5. Apr 21, 2017

### Staff: Mentor

Moderator's note: I have edited the title of this thread to be more descriptive of the specific question.

6. Apr 21, 2017

### John Clement Husain

Are there any equations for it? I haven't seen any study done online yet....

7. Apr 21, 2017

### Staff: Mentor

The stress-energy tensor for a perfect fluid is well known; see, for example, here:

https://en.wikipedia.org/wiki/Perfect_fluid

The presence of sound waves just means the pressure $p$ and density $\rho$ of the fluid are functions of position and time.

8. Apr 21, 2017

### John Clement Husain

OH THANK YOU VERY MUCH

9. Apr 21, 2017

### Paul Colby

Actually, I've just completed a maxima calc for the transverse traceless gravitational radiation from any (well in principle) general time harmonic stress tensor. Basically, only shear waves in a material emit gravitational waves. When I feed my calc a diagonal pressure wave, I get 0 gravitational radiation. So my answer is no. Compressional sound waves do not radiate. Shear waves will however.  This is in the linearized theory of course.

10. Apr 21, 2017

### Staff: Mentor

That's not what he asked. He asked if sound waves curve spacetime. Emitting gravitational radiation is not the only way for something to curve spacetime.

11. Apr 21, 2017

### Paul Colby

However, in the time harmonic case for weak fields I bet by far the most significant contribution are the near field effects which go like $1/(kr)^{5}$. Only the $1/kr$ terms are radiation proper. So for a sound wave I think this is the answer to his question. If not I'd like to know.  even these near fields are 0 for scalar pressure waves.

12. Apr 21, 2017

### Staff: Mentor

No, by far the most significant contribution is the energy density of the medium, including the energy density contained in the sound waves. That is going to be many, many, many orders of magnitude larger than any gravitational radiation.

The next most significant contribution by far is going to be the pressure of the medium, including the pressure caused by the sound waves. That, while many orders of magnitude smaller than the energy density, is still going to be many, many orders of magnitude larger than any gravitational radiation.

13. Apr 21, 2017

### Paul Colby

Yes, $mc^2$ will always win for the static component. Not my point.

14. Apr 22, 2017

### Staff: Mentor

Not mine either. My point is that the energy density will cause many, many, many orders of magnitude more spacetime curvature than the gravitational waves you are talking about (with pressure in second place, still by many, many orders of magnitude). And the OP was asking about spacetime curvature.

Also, the energy density and pressure in question are not static. They are time-varying, because there are sound waves present.

15. Apr 22, 2017

### hilbert2

You'd need to have a quite high-amplitude pressure wave to cause relativistic effects...

16. Apr 22, 2017

### John Clement Husain

Say, if space is like water,
then can we safely say that if we shoot a low frequency sound in a single point it will be able to create a spatial whirlpool?

17. Apr 22, 2017

### Ibix

It's spacetime that curves in general relativity, not space, and it's not like water.

What Peter was saying is that a pressure wave in water or air (or whatever medium) means changes in the energy and stress distribution in the matter, and that means changes in spacetime curvature. He wasn't saying that spacetime itself supports sound waves.

You can get waves in spacetime. These are called gravitational waves, but they don't have much in common with sound waves.

18. Apr 22, 2017

### John Clement Husain

Hmm, I do understand that space is basically the thing that encompasses everything (Like why are you shaped like that? Why is a door shaped rectangular? etc.) but what I meant was about the matter in space. Is it PLAUSIBLE, if not possible, to create such phenomenon in my previous statement?

19. Apr 22, 2017

### Ibix

Spacetime is the relevant thing. It isn't generally possible to separate it into space and time in a unique way.

I'm not sure what you are trying to describe, but I would just point out that gravitational effects due to the rotation of the entire Earth are only detectable after months of integration time (look up Gravity Probe B). So I very much doubt that a mass of air in motion at soundwave speeds would produce any gravitational effect detectably different from a stationary mass.

20. Apr 22, 2017

### John Clement Husain

Ah, I see.... thank you!