Playing music with Gravitational waves

[Xforce]

TL;DR Summary

Are gravity waves audible, if they are strong enough?

Seems gravity waves are longitudinal waves, similar to sound waves as it is produced by the vibrations of spacetime? So in theory, if we can produce a powerful enough gravity wave, can we hear it?
G-waves are usually produced by merging binary neutron stars or black holes. These celestial bodies are too far away from us to receive any audible waves, in fact one of the most accurate and giant machines such as LIGO was made to detect it. So if we can produce our own gravitational waves, for example by vibrating a very dense string that is able to bend spacetime, such as one made of neutron degenerate matter that is a few nanometers wide (otherwise it’s too heavy!) will we be able to broadcast music and other audio using gravitational waves, and allow everyone to hear without a radio? Or this may boost our research for SETI?

 

[Ibix]

Seems gravity waves are longitudinal waves,

No. Gravity waves are transverse waves on the surface of a fluid. Gravitational waves (which are what you seem to be talking about) are also transverse waves.

I don't think you could directly hear gravitational waves. I can't see how they could significantly vibrate your eardrum.

You could certainly produce modulated gravitational waves in principle, but you can't get any significant power out of anything less than a couple of neutron stars (a "dense string" won't cut it, even if there were some way to make it of neutronium, which I'm pretty sure isn't plausible). Modulating the motion of a couple of stars is left as an exercise for the reader.

 

[Xforce]

I thought gravity waves are like the vibration of spacetime... and they should be audible even in the vacuum...
Of course I can be incorrect, but this is just a hypothesis.

 

[Ibix]

I thought gravity waves are like the vibration of spacetime...

Gravitational waves are, yes. Gravity waves are a type of water wave. The terminology is unfortunate, but we're stuck with it.

and they should be audible even in the vacuum...

Gravitational waves travel through vacuum, certainly. But that doesn't mean you can hear them. I think your eardrum needs to be pushed backwards and forwards relative to your head (and it needs air!) for you to be able to hear anything. That isn't the kind of motion gravitational waves induce, even if they were strong enough to produce a detectable motion (which means a billion billion times stronger than the ones we have detected to date).

 

[Xforce]

So... if gravitational waves push spacetime back and forwards, will it just push the objects on the way back and forwards?
An area of spacetime carrying objects within that area can have more applications, such as a warp drive, and a gravitational wave microphone.
The ones we detected using enormous instruments are emitted from thousands of light years away, even from other galaxies. How can we expect the signal strong enough to be audible? It makes a huge difference if the source of the waves are less than a few kilometres.

 

[berkeman]

Mentor Note -- clarified "gravitational waves" in the thread title...

 

[pervect]

If you positioned someone's head correctly, gravitational waves could make someone's eardrum's vibrate. So I would expect that they'd be audible in that case if they could be strong enough.

We can use the sticky bead argument, https://en.wikipedia.org/wiki/Sticky_bead_argument to justify this approach. Hear the moving eardrums are modeled as being like beads that are free to slide along a rigid rod.

Put the left ear on the middle left of the diagram below, the right ear on the middle right.

How far would the eardrums have to move before you could hear the sound? A not-very-educated guess is a micron or so. The first Ligo detection would move then by the distance between the eardrums * 10^-21, call the distance between eardrums 1/3 of a meter. That means that the first Ligo event as detected on Earth would move the eardrums about .3 * 10^-22 meters. That event was 410 megaparsecs away, about 10^25 meters. So you'd need to boost the signal by a factor of 3*10^16 or so. If we ignore the near field, I think that means you'd need to reduce the distance by a factor of 3*10^16, but I haven't looked this up to double check , my memory on the point could be faulty. Some of the other assumptions may be a bit off-the-cuff as well.

 

[PeterDonis]

Some of the other assumptions may be a bit off-the-cuff as well.

There's one factor you did not take into account: the eardrums are not free to move the way the LIGO test masses are. Eardrums are subject to internal forces that constrain their motion. This will decrease the distance they move as compared with the distance the LIGO test masses move. (Note that the sticky bead argument similarly requires friction between the beads and the rod, which will reduce the distance the beads move in response to a given GW as compared with LIGO test masses. Avoiding such dissipation and damping of the motion is why LIGO uses an interferometer and has such an elaborate system in place to isolate the test masses.)

How much will internal forces decrease the motion? Off the top of my head I would say by a factor of order unity--say a factor of 2. So quantitatively it probably doesn't make a great deal of difference. But that assumes that the internal forces are fairly weak. Strong internal forces could produce a much greater decrease--this is one of the things that makes bar detectors of gravitational waves impractical as compared with interferometer detectors like LIGO.

 

[Ibix]

We can use the sticky bead argument, https://en.wikipedia.org/wiki/Sticky_bead_argument to justify this approach. Hear the moving eardrums are modeled as being like beads that are free to slide along a rigid rod.

I don't think that's an appropriate model, though. As I understand it, the eardrum is attached to the skull at its rim - it's not just free to slide backwards and forwards in your ear canal. It flexes (like a drum skin) when sound enters the ear. So to be excited by a gravitational wave you'd need biologically noticeable strains over whatever the thickness of the eardrum is. I'd think that kind of thing would be Earth shattering, literally.

 

[A.T.]

It flexes (like a drum skin) when sound enters the ear. So to be excited by a gravitational wave you'd need biologically noticeable strains over whatever the thickness of the eardrum is.

The eardrum is relevant for hearing sound. A gravitational wave that passes through your body could excite your inner ear directly (the ossicles or the cochlea). But the required intensity would probably cause sensation throughout your body.

 

[pervect]

I don't think that's an appropriate model, though. As I understand it, the eardrum is attached to the skull at its rim - it's not just free to slide backwards and forwards in your ear canal. It flexes (like a drum skin) when sound enters the ear. So to be excited by a gravitational wave you'd need biologically noticeable strains over whatever the thickness of the eardrum is. I'd think that kind of thing would be Earth shattering, literally.

The model is probably oversimplified. The skull is more rigid than the eardrums, so I'd expect that the skull stretched very little due to the tidal force of the gravitational waves, while the eardrums moved considerably more. I will agree, as you and Peter point out, that I oversimplifed the model without discussing the assumptions.

If one wanted to do a more formal analysis, one could compute the Riemann tensor of the gravitational waves in an orthonormal basis. I'd expect that the electrogravitic part of the Bel decomposition of the Riemann tensor would be the only significant part. This components are what I earlier referred to as the "tidal forces" of the gravitational wave.

However, if one isn't comfortable with the Bel decomposition, one could probably use an approach based on the geodesic deviation equations. Because the velocity of the eardrum is low, though, the only significant components should be the same ones that I identified as the "electrogravitic" ones.

To do the Bel decomposition, one needs a unit timelike vector field representing the "time" vector of the observer who is "listening" to the gravitaitonal waves, which we will call $\hat{t}$.

Then there is a 3x3 matrix that represent the tidal forces, $R_{\hat{i}\hat{t}\hat{j}\hat{t}}$, i,j=1..3.

These can basically be interpreted as a force/unit mass that is applied to all parts of the ear and skull.

It's really just a guess that the eardrums move relatively freely, and the skull does not, but that's what I'd expect would happen. I don't have a detailed model of the elastic properties of the ear or the skull, but my intuition says that the skull is pretty rigid, and that we won't be off by more than a factor of 2 or 3 or so if we ignore the elastic forces on the eardrum and assume they are free-flooating. A purely Newtonian analysis of an elastic body is all that's needed though - the hard part of the problem is not the GR part, but finding an elastic model of the ear to calculate it's response to the tidal forces.

https://en.wikipedia.org/w/index.php?title=Bel_decomposition&oldid=814235481