The sound will mostly depend on the atmosphere, on the moon there would be no sound at all, no air for the sound weaves to move through, extremely cold/hot too, depending on how you look at it.
On Mars, the atmosphere is very very thin, on Venus it's very very thick, on Mercury there barely is an atmosphere.
How it will affect the sound I donno, but the pressure and temperature differences on these worlds is of much greater concern then how the headphone will sound.
On Venus the headphone would melt, so no sound, on Mercury it's the same deal, at least during the day, at night they would freeze as if dipped in liquid nitrogen.
On Mars you might be able to make headphones work during to summer in areas of low elevation where temperatures at ground level go above freezing.
As for the sound, since the atmosphere is thin, I guess the voice of a person who inhaled helium might be a good hint as to how it would sound.