Lighting creates thunder by manipulating air - heating it up a lot causes it to rapidly expand, making a shockwave that we perceive as sound.
Thunder is the sound caused by lightning. Depending on the distance
and nature of the lightning, it can range from a sharp, loud crack to
a long, low rumble (brontide). The sudden increase in pressure and
temperature from lightning produces rapid expansion of the air
surrounding and within a bolt of lightning. In turn, this expansion of
air creates a sonic shock wave, similar to a sonic boom, often
referred to as a "thunderclap" or "peal of thunder"
So it would definitely possible for your character to make a loud noise in a similar way. It would be a new noise, with the energy of the sound wave conferred on its creation, just like thunder.
Amplifying an already produced sound on the fly would be super tricky. That sound wave (vibrations in the air) already has the energy it was imparted on its creation. Your character could accelerate the transit of a sound to its target by making intervening air more dense (the denser the substrate the faster the sound wave) but that does not make the wave itself more energetic.
If you want to make a sound more energetic you can convert it to some different medium (like electrical impulses for an electric guitar or scratches on a hard surface like a phonograph record) then recreate it louder. An existing traveling sound wave is a series of pulses of relatively compressed and uncompressed air. Augmenting the energy of that would mean perceiving the nature of these pulses as they travelled by and augmenting / refining them on the fly. Tricky! Sound waves are air so maybe your character could do this, but it seems super fussy for use as an offensive weapon if your character can just create a fresh gut-loosing burst of thunderous brown notes.
But if there were informational value in the sound wave it might be worth the effort - for example your character murmurs "your mama" and then augments and refines the traveling sound wave he has made to make sure his target hears it whispered right in his ear.