In this Answer I suggested that an animal could have a tampani acting as a loudspeaker, as in Vernor Vinge’s The Blabber, later featured as the race called Tines in A Fire Upon the Deep. In the original Blabber it was shown that the animal could reproduce any sounds it had collected, like a mockingbird or lyrebird. The use of a structure that’s essentially a loudspeaker allows playback of any waveform within the bandwidth of the speaker. (In the referenced post, separate woofer/tweeter and resonance cavities extend the total bandwidth. That’s not important to this question.)
This begs the question: how can such a natural loudspeaker work? The membrane is no problem, nor is a stiff ring to set it in. But how does the driver work? It is doubtful that they could evolve an electromagnetic voice coil though I'm certainly interested in answers that would explain the biology and evolutionary pathway of that.
More generally, how could it work (e.g. using muscles) and be able to playback an arbitrary waveform? Note that the Tines in particular used ultrasonic sound for their group mind, so let’s say it handles up to 30 kHz.
Normally vocal cords and the like will simply use muscles to tension a string and then it vibrates at the natural frequency. That can give a repeating wave train of a fundamental and harmonics, but the muscles don’t have to respond on the speed of the sound’s frequency! To simply use muscles to actuate a voice coil would require speed beyond any muscle tissue we understand.
I would also be interested in biological adaptations of “alternative” speaker designs such as electrostatic and magnepan — it doesn't have to be exactly analogous to a compact central voice coil driver.