Learn English – “Enact Change” – Is it correct

Andrew Neely is close, but not quite there:

"Fluctuates widely" means the standard deviation (possible ranges, whatever) is (relatively) huge.

"Fluctuates wildly" means the standard deviation isn't necessarily huge, but it wavers between its two extremes very often.

What you have is a punnet square of possibilities: Not widely and not wildly, just widely, just wildly, and both widely and wildly. Choosing whether to use "widely" or "wildly" in speech depends first on whether both apply, and then on which one you want to draw attention to.

EDIT: Jefromi brings up a good point in the comments, that while "wildly" doesn't mean "widely", it's not often used for small, rapid fluctuations. So I'll include a third option that embodies that description: "fluctuates rapidly".

Strictly speaking it's damp - OED: to stifle, choke, extinguish; to dull, deaden (fire, sound, etc.)

As a child, it was my job to damp the fire (9600 hits in Google Books) every night by closing off the stove's air supply. If I did it right, next morning I'd just add more coal and open the air vents. If not, I'd have to clean everything out and relight it with paper and kindling.

According to OED, damp/dampen have a common origin - which is somewhat uncertain, but the key concept seems to be smoke, dust, vapour, steam. Today, damp is more closely associated with moisture/water, whereas dampen goes more with stifle/extinguish.

It's worth noting that dampen the fire gets 5310 GB hits (i.e. - the "incorrect" usage occurs relatively more often with fire than with sound). Partly that's because some people think in terms of adding dampness/water, rather than taking away air, to slow down a fire. But partly it's because they're essentially the same word anyway, so neither is really "wrong".