As a historian, my physics is awful, so excuse me if I sod this up completely!
My understanding of this is that the sound would not be "dampened" so much by a low atmospheric pressure as it would slowed, so sound would likely take a lot longer to reach you than it would on earth, but as far as I know there is little to quieten it down at all. Additionally, the speed of sound is far less affected by air pressure than it is by the temperature of that air, sound being "transferred" between vibrating gas molecules which have far less energy to vibrate (and therefore do so less quickly) when that gas is cold. And Mars is cold. Really, really cold.
So! In answer to your (implied) question, no. I think that the sounds on Mars would be roughly the same volume as they are on earth, but would reach you far slower as a combined result of the low air pressure and the low temperature of the red planet.
Apologies if that's utterly wrong.