Gravitational waves obey the inverse-square law much like most radiation does (and subject to some constraints about weird spatial geometry, but most of their propagation is going on in open flat-ish space, so we can ignore that).
GW150914, the first gravitational wave observed, had an amplitude of about 4 times 10^-22 [1], i.e., differences changed by a factor of about that. Typical sound displaces the eardrum by on the order of half a micron or so [2], with the threshold of hearing at about 100 nm. The inner ear's shape is curved, but linear length is on the order of 10 mm [3] (it curves around so the total length is longer, but the gravitational wave would be transverse along its length).
A 100 nm displacement on a 10 mm length is a relative change of (100 x 10^-9) / (10 x 10^-3) = 10^-7, that is, 4 times 10^-17 times larger than the gravitational wave detected. That gravitational wave was emitted at a distance of about 410 Mpc [1], and so we can solve:
(d / 410 Mpc)^2 = 4 x 10^-17
d^2 = 4 x 10^-17 * (410 Mpc)^2
d = 2 parsec.
Granted, this is at the limit of hearing for a very brief sound (the sound was only in the human audible range for about a tenth of a second). You'd need to be perhaps 10 times closer - about 20,000 AU - for it to be a loud sound under these assumptions.
Of course you wouldn't be around to hear it for very long because you're 20,000 AU from one of the most energetic events in the cosmos, but hey, you'd hear a brief "click". Totally worth being vaporized.
EDIT: the CALCULATIONS are right, but they're based on an incorrect assumption. As a poster further down this thread corrects me, while the energy of a GW obeys inverse-square, the amplitude is just inverse. I can't edit my original post, but the corrected calc is here.
There is also a typo in my post where there's 10^-7 instead of 10^-5, but the calculations are done correctly.
That corrected assumption gives:
d_audible / d_actual = 4 x 10^-17 x 410 Mpc = about 500,000 km
or about the distance to the Moon.
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<rest of post deleted since it was based on an incorrect premise>
Sorry I hyperfocused on the value but it's really the context which makes it confusing:
> 10^-7, that is, 4 times 10^-17 times larger than the gravitational wave detected
which doesn't sound right. (Like saying "X is 0.1 times larger than Y" when X = 10Y.) The ear displacement is 2.5×10^16 larger than the gravitational wave, no?
(Also I think 10^-7 should be 10^-5 in the quoted phrase, as per your reply above.)
> (Also I think 10^-7 should be 10^-5 in the quoted phrase, as per your reply above.)
Yeah, you're right, I had a typo in one of the intermediate numbers (the rest of the calcs used the correct number). Turns out I was just wrong overall though, not because of a typo but because of an incorrect assumption. Energy goes as 1/r^2, but amplitude is only 1/r, so the correct value is much smaller (it's about the Earth-Moon distance).
> 10^-7, that is, 4 times 10^-17 times larger than the gravitational wave detected which doesn't sound right. (Like saying "X is 0.1 times larger than Y" when X = 10Y.) The ear displacement is 2.5×10^16 larger
A is 2.5x10^16 larger than B is equivalent to B is 4x10^-17 larger than A, although I get what you mean by the phrasing being weird. "times the size of" would've been better than "larger".
Oh. Well, silly me. I did double check that it's inverse-square, but apparently not deeply enough - the energy is, but the amplitude isn't. Which makes sense if I think about it a little more (it's basically a spring, so energy ~ displacement^2)
They do. The signal in question peaked at around 250 Hz, so in the bass range of human hearing.
But as noted in other posts the post you're replying to was based on an incorrect assumption - there's a corrected value in one of the comment threads, and the distance for it to be audible is much closer than originally posted, roughly the Earth-Moon distance.
On this point I recall when the gravity wave detector first detected a black hole merge, which is of course a LOT of mass and power. It was in the hearing range so they played a .wav. It unironically sounded exactly like a "PLOP" drop of water falling in a bucket - an irony that such a big event and a small event sound so similar.
Gravitational waves obey the inverse-square law much like most radiation does (and subject to some constraints about weird spatial geometry, but most of their propagation is going on in open flat-ish space, so we can ignore that).
GW150914, the first gravitational wave observed, had an amplitude of about 4 times 10^-22 [1], i.e., differences changed by a factor of about that. Typical sound displaces the eardrum by on the order of half a micron or so [2], with the threshold of hearing at about 100 nm. The inner ear's shape is curved, but linear length is on the order of 10 mm [3] (it curves around so the total length is longer, but the gravitational wave would be transverse along its length).
A 100 nm displacement on a 10 mm length is a relative change of (100 x 10^-9) / (10 x 10^-3) = 10^-7, that is, 4 times 10^-17 times larger than the gravitational wave detected. That gravitational wave was emitted at a distance of about 410 Mpc [1], and so we can solve:
(d / 410 Mpc)^2 = 4 x 10^-17
d^2 = 4 x 10^-17 * (410 Mpc)^2
d = 2 parsec.
Granted, this is at the limit of hearing for a very brief sound (the sound was only in the human audible range for about a tenth of a second). You'd need to be perhaps 10 times closer - about 20,000 AU - for it to be a loud sound under these assumptions.
Of course you wouldn't be around to hear it for very long because you're 20,000 AU from one of the most energetic events in the cosmos, but hey, you'd hear a brief "click". Totally worth being vaporized.
[1] https://en.wikipedia.org/wiki/First_observation_of_gravitati... [2] https://biology.stackexchange.com/questions/79963/how-far-do... [3] https://www.verywellhealth.com/inner-ear-anatomy-5094399