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Sufficiently powerful gravitational waves can excite an eardrum and be heard. How powerful would the waves have to be for a human to actually hear them, and what would be the side-effects of that intensity of gravitational radiation?

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No, not really. There are a number of factors for why you can't:

  1. As duly pointed in the comments, you 'hear' something when the eardrum moves with respect to i.e. differently from your body. If you are in the middle of a wave, then you body is deformed in the same way as your eardrum. Also, there is the fact that the disturbance caused by the waves themselves are in the order of magnitudes of the size of an atomic nucleus. There is no way our eardrums can detected that (more on that in point 2). So, you can't hear the wave itself.
  2. Gravitational waves tend to have very low frequencies (corresponds to long wavelengths). According to an answer here, the maximum frequency of a gravity wave is proportional to $\sqrt{G\rho}$, where $\rho$ is the density of whatever object released the waves. Waves which have longer wavelengths just pass through an object smaller than it's wavelength (Though it has been pointed out in the comments below, that we can hear sounds of wavelength $17$m). Keeping in mind the usual wavelengths of gravity waves, (and the size of the ears), to hear a gravity wave would require a ridiculously large amount of energy. The disturbance caused by any regular gravity waves is in the order of magnitudes of an atomic nucleus. Our eardrums are not built to be that sharp. So, if the gravity wave has to 'disturb' our eardrum, it needs humungous amounts of energy. And that energy has to be produced by something having $\rho$ more than anything we have ever detected or hypothesised. (And such an event of high energy, may as well destroy Earth itself; not by gravity waves, but by other forms of radiation or free energy)
  3. The most important point: gravity waves don't work that way. The eardrum vibrates when any sound wave applies pressure on it. Gravity waves are not like conventional waves: they don't apply a pressure on anything. In fact, they just stretch and compress space itself, and that does not inflict any pressure on an object. If your ear is anywhere near a gravity wave, the eardrum would be squished and squashed, which is not the equivalent of a vibration caused by a sound wave. If you want to know more about how the gravity wave stretches and compresses space, take a look at my answer here: How can we imagine gravitational waves?

So, that is why you could not 'hear' gravitational waves.

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  • $\begingroup$ This answer is wrong. Humans can hear sounds with a frequency as low as 20 Hz, which corresponds to a wavelength of about 17 m – much larger than a human body. Also, if you think gravitational waves cannot apply pressure to an object, how do you think LIGO is able to detect them? "Squishing and squashing" an eardrum does create vibrations that can be detected by the cochlea. $\endgroup$ – Thorondor Jun 22 '20 at 18:06
  • $\begingroup$ You have misunderstood how LIGO works. The lasers there are not directly influenced by gravitational wave pressure and deflected by them. Instead the squishing and squashing causes a delay in the arrival of the lasers. It is sort of 'not okay' that you are just commenting and/or downvoting based on wrong opinions. Your second point may hold but there is the point that the ear cannot detect such small changes . Still, it is just incorrect to say that the answer is wrong and imply that you can hear gravity waves. $\endgroup$ – PNS Jun 23 '20 at 6:59
  • $\begingroup$ LIGO's arms actually change length under the influence of gravitational waves. That is, the mirrors move closer together and then farther away. As the LIGO website says, "gravitational waves make themselves known through vibrations in LIGO's mirrors." This is obviously a simplification for a general audience, but it's not wrong. $\endgroup$ – Thorondor Jun 23 '20 at 8:19
  • $\begingroup$ As for your second point, you're right that the ear cannot detect gravitational waves as small as the ones LIGO measures, but that wasn't the question. A sufficiently powerful gravitational wave would absolutely be audible to a human ear, which is why your answer is factually incorrect. $\endgroup$ – Thorondor Jun 23 '20 at 8:20
  • $\begingroup$ Yes, the arms of LIGO do change length, but its not because the waves themselves are applying pressure to compress them. It's because the space itself contracts along with everything in that space. I am not saying anything about simplification or complex reality, I am saying that pressure is different from space contraction. Also, refer to my edited answer for your second query. $\endgroup$ – PNS Jun 23 '20 at 8:33

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