I believe when you are referring to sound you should use "damping" or "damper". The two sound similar, but "damping" should always be used in the context of sound, gas or fire.

Damping: to check the vibration or oscillation of (as a string or voltage) (Miriam Webster Dictionary)

Whereas "dampening" has a less scientific meaning:

• to check or diminish the activity or vigor of : deaden ("the heat dampened our spirits")

• to make damp ("the rain shower barely dampened the ground")

I believe when you are referring to sound you should use "damping" or "damper". The two sound similar, but "damping" should always be used in the context of sound, gas or fire.

Damping: to check the vibration or oscillation of (as a string or voltage) (Merriam-Webster Dictionary)

Whereas "dampening" has a less scientific meaning:

• to check or diminish the activity or vigor of : deaden ("the heat dampened our spirits")

• to make damp ("the rain shower barely dampened the ground")