What would a gravitational wave sound like up close?

LIGO Sensitivity

Actual sensitivity of the LIGO detectors (H1 = Hanford, L1 = Livingston) at a range of frequencies. Image credit: LIGO Scientific Collaboration

The gravitational waves detected by LIGO tend to be in the frequency range of a few tens of Hertz to a few hundred Hertz. That’s not just a coincidence – it’s the frequency that LIGO is designed to operate at, and that in turn is because that’s the frequency at which it’s expected that some of the most common relatively powerful gravitational wave sources in the sky occur at. It’s also a feature of the design of the instrument, with higher frequencies limited by the laser power (more photons = more sensitive) and lower frequencies limited by things like the seismic isolation, thermal variations in the mirrors and suspension, and a range of other things. If you are interested in finding out more, you should play Space Time Quest.

Because frequency range to which LIGO is sensitive is is within the human hearing range, it’s possible to convert the gravitational wave signals directly into sound. They’re often a bit low, so it’s common to shift them up in frequency – it can be that’s not really any different from shifting infrared data into the visible to make an image we can actually, well, see! The result, in the case of GW150914 (the first gravitational wave detection) is a sound like the one below.

LIGO-Hanford data, shifted up in frequency by 400 Hz. For more see the LIGO Open Science Centre (scroll to the bottom for audio files)

But what would it actually sound like?

But converting a signal to audio isn’t really the same as hearing what it would sound like. With radio astronomy, it’s also possible to convert the signals from things like pulsars into sound waves, the idea being that that is what would happen if you tuned a sensitive enough radio into the right frequencies – arguably, that’s what radio astronomy is, but instead of playing out of a speaker the data is recorded on a computer.

But with gravitational waves it is, in principle, actually possible to hear the sounds. The gravitational wave stretches a squeezes space, and the resulting pressure change is essentially the same as a sound wave (though the pressure would increase in one direction and decrease in another, so I’m not 100% clear on how that would actually sound). The problem is that they’re much too weak – with distances (and so pressures) changing by around 1 part in a thousand trillion trillion (10-21).

But what if it were even closer?

The strength of gravitational waves drops off with distance, so if we were closer, the amplitude of the waves would be stronger. Although the power drops off with the typically “inverse-square” law, the amplitude drops of linearly.

So what if the binary black holes that produced GW150914 were at, say, a distance of 1 astronomical unit (the distance from the Earth to the Sun, or 150 million km). Compared with their measured distance of 1300 light years (give or take a factor of about 2!), that’s about a factor of a hundred million million (1014) – so the amplitude of the gravitational waves would be about 10-7 – one ten millionth.

That doesn’t sound like a lot, but sound waves are pretty weak. The threshold of hearing is equivalent to a pressure change of just 20 μPa – or 200 trillionths of atmospheric pressure (which is 1 bar, or 100,000 Pa). A change of 10-7 in pressure therefore corresponds to about 10 mPa – so considerably higher than the threshold of hearing.

The scale of sounds is the decibel (dB) scale, with 0dB being the threshold of hearing (that 20 μPa pressure change). The ear (as with many things, including the human eye) responds in a logarithmic way, which means that things that are actually much, much louder don’t deafen us. The pressure change is related to the dB scale by dB = 20 log10(ΔP/ΔP0) – where ΔP is the measured pressure change and ΔP0 is the reference value (in this case 20 μPa).

By that reckoning, the pressure change at a distance of 1 astronomical unit would be equivalent to around 50 dB – that’s about the same loudness as an air-con unit, or a normal conversation around a metre away (at least according to Wikipedia). That would probably be quite hard to pick out over the general hum of your spacesuit or spaceship.

Let’s get closer!

What if we approached to the same distance as the Moon (around 400,000 km). The volume then would be about 100 dB, or the same volume as a jack hammer a metre away. I think you’d notice that, though the signal is only very short (about 200 ms). Also, your spaceship engines would be firing like crazy, trying to counteract the 5000g pull from 62 Solar Mass black holes now sitting a little too close for comfort…

The threshold of pain (140dB, corresponding to a 0.2% pressure change) would be reached at about 4000 km distance. That’s pretty close, and probably not observable for a couple of reasons, both related to the fact that you’d be long dead. Firstly, the LIGO signal shows the final five or so orbits of the black holes, and at the start of that they’re about 3000 km apart, so if you were just 4000 km from the common centre of mass you’d presumably have just been passed by a 30 solar mass black hole moving at a fair fraction of the speed of light.

Secondly, the gravitational pull from 62 Solar Masses would be equivalent to 50 million g. If you’ve got a powerful enough engine, that’s fine, but the tidal forces would kill you. The difference in gravitational pull (the tidal force) between your head and your feet (assuming they’re about 2m away) would be equivalent to 26g – certainly not survivable.

Assuming you had some sort of magic anti-tidal machine (on top of the anti-gravity machine) then you’d hear the collision of the black holes as a painful, low thud. However, the drop in mass of the black holes due to the loss of energy in the collision (equivalent to 3 solar masses) would mean that the change in gravitational pull at the moment of the collision would be around 1g – it would feel (very briefly, for a few milliseconds) like you were in a falling lift.

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