Many "no moving components" machines do make noise: various transformers are notorious for that. Perhaps our fictional explanation could be found in coils and fields?
I think many of the setting designations heard in Trek are in fact overlapping, meaning either the same thing or elements of the same thing. That is, there aren't just four or sixteen notches to a single control lever: there are several parameters to adjust, this in part contributing to the menagerie of setting designations we hear used.
That doesn't work. The phaser hits your jacket, but doesn't vaporize just that. It vaporizes the jacket, the shirt, wristwatch, necktie, undershirt, you, your hat, your boxers, pants, contents of your pockets, garters socks, shoes, insoles, yet "knows" to stop at the pavement, which is as connected to the shoes as the socks are.
And it doesn't stop at
air, which is also connected.
ST6:TUC really gives a nice explanation: the effect, once inserted into the mass that is the victim, propagates until it hits a sufficiently high phase boundary. That is, it proceeds until it hits massively denser or massively less dense material. Clothing is close enough to the human body to be consumed by the effect, but air or walls are not. Similarly, an effect inserted into a steel kettle won't make the jump into mere water inside.
Not all phaser effects manage to reach the phase boundary, of course. If one fires at a vast wall of rock, the effect only spreads out so far until fizzling out; people using phasers as rock drills make use of that, adjusting their settings so that crawling-height or walking-height ciruclar tunnels are the result. Similarly, one may fire a weak effect into a human body so that it only consumes the internal organs but leaves the body more or less okay.
All we have to assume now is that phasers (not being based on having something explode inside like today's sidearms) are made of a relatively "soft" material that doesn't differ much from the human body or the human clothing. The barrel may be configured so that a phaser doesn't destroy itself with each and every shot, but if the effect propagates back along some other conduit such as the hand holding it, the barrel coating is of no help and the whole thing (or enough of it) is phased out of this realm.
We might, for the sake of convenience, also assume that when hitting a phase border, a potent effect will make disappear
some material from a different phase, such as metal coins in the pocket but not the entire metal manhole cover beneath the shoes. The TOS make-disappear kill beams are deliberately defined as featuring just a tad of overkill, so that the death is maximally merciful and assured but collateral damage unlikely. The TNG beams are less humane when used in wars (where saving of power is a concern) or crimes (where mercy is undesirable).
Timo Saloniemi