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We know that space cannot spread a sound wave as there is no "air" or a medium that would support the spread of a sound wave. However if we put ourselves in the vicinity of an exploding star, would it be possible to hear something?

The question arises from the idea that within the explosion of a star (first few seconds or less) you may hear a noise due to the explosion of the star...

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Sound is a longitudinal compression/rarification wave; these things can't really be said to exist unless the wavelength is much longer than the mean free path in the medium. In space the mean free path is going to be very, very long even is a dense nebula.

So the first, reasonable answer is very, very low pitch and low volume.

The shock wave, of course is denser and can support shorter wavelengths, but these are still going to be below human hearing.

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If you were close enough to be hit by a significant amount of something (material or just radiation) being ejected from the star, then you would probably hear it hitting the walls of whatever is keeping air around you (spaceship, space-suit, whatever).

This would not last very long though, since the noise would be the sound of cracking or boiling or burning (depends very much on the materials), and then you die. :D

If you are close enough, you would be just vaporized and I doubt your brain would have the time to process any sensation of sound.

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If you were close enough, then yes, you'd probably be hit by the wave of outgoing ejecta, which I suppose would register as sound. To give you some idea of the intensity, typical Type Ia supernovae (those that come from a white dwarf being overloaded with too much mass) eject material into the surrounding environment at over 10,000 km/s.

Moreover, the immediate vicinity of a supernova is often anything but vacuum. There can be a dense circumstellar medium consisting of gas thrown off by an aging giant star just before it undergoes typical core collapse (leading to a Type II explosion). Or there could be an accretion disc around a white dwarf (artist's depiction here) that is stripping matter off an inflated companion star.

EDIT: Based on dmckee's response, I would agree that you have to consider the properties of whatever specific medium you're dealing with, especially its density, to determine if sound waves of audible frequencies can propagate.

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