Sorry, my wording was unclear. I mean asymptotically approaching zero, as opposed to, say, going to zero in a straight line and then switching to a constant zero once you get there (thereby creating a discontinuous derivative).
Indeed, I imagine that is what is going on. The straight line case is what the loudspeaker driver will do in reality if you send it a discontinuity, and that's what produces the pop.
Smooth interpolation will avoid a really nasty pop, but in the real world, musical waveforms are highly complex, so any interpolation algorithm, however smooth, will produce some kind of artefact if you chop the wave in the middle of a cycle and smooth it to zero.
This can be observed when setting loop points in a sampler - you are usually provided with tools to help you match the loop points to the zero crossings. This is not enough however to remove all artefacts. Only some zero crossings will do: one has to match the higher-order cycles in the waveform as well. I don't really have the mathematical vocabulary to really describe what I mean here, but hopefully it's clear.
(BTW when I say driver in these posts I mean the magnet-and-cardboard-cone assembly in the speaker, not any kind of software.)
That's not how sound works. Think of a vibrating object. If it stops vibrating suddenly, slowly moving it to its center point isn't going to make the absence of vibration any less jarring.
Indeed. I think that's what I'm trying to describe in my sibling comment to yours.
However, what it will successfully avoid is the loudspeaker driver attempting to instantaneously snap from some nonzero x-position back to it's origin, which is what causes the really nasty clicks.
