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".

Strain drops off as 1/r, not 1/r^2

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)

For other readers, this poster's correction is right, here's an astronomy SA thread on it. https://astronomy.stackexchange.com/questions/34761/why-does...

I swear, the one time I try posting outside my areas of expertise :D