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It does. We can't hear it, but it does.
Well, I think technically it doesn't. There's no medium to propagate pressure waves, so at no point would the mechanics of sound actually exist, I would think.
The sun itself is a medium that can propogate sound waves. Someone standing on the Moon could equally well make the case that there is no medium to propagate pressure waves from the Earth, so the Earth must not make a sound.
Aye, true. Though I would consider that case different (slightly, but not fundamentally wrt waves existing) from the sun because on earth there are atmospheric sound waves that just don't reach out to the moon. But I hadn't thought of the possibility of waves going into the sun, so there would be existing waves there too. More akin to making a sound on the moon by vibrating the moon itself I suppose.
Edit: and really, I'm talking out of my ass lol. There could very well be gases or some such to vibrate around the sun, even coming out of the sun and carrying vibrations, but I don't know enough.
The sun has an atmosphere so there are soundwaves coming out of it. It's actually all one big atmosphere getting thinner and thinner as you go out just like ours.
That makes me wonder where the sun ends and it's atmosphere begins! Stars are weird.
Technically there is no boundary, it's atmosphere all the way in. But what we might call the "surface" is the photosphere. That is where the density becomes "low" (read not insanely high) enough that light can escape in a free path.