Yes, we agree on most everything and my understanding of both physics, mechanics and biology seem to agree with yours.

I guess the one main disagreement is if a pulse, either single or repeated, might potentially be more harmful than a sine wave of a single frequency. According to the teachings I’ve had, or my recollection thereof, a pulse or impulse may carry the sum (or zero sum) difference if any ramping wave, but the nature of the impulse it literally hits differently. A transition of difference in state versus a forceful immediate change. A push or a slap. Or a push and pull versus a slap and yank, should we speak of a complete cycle.

This was what I attempted to illustrate with the plunger example. If you are familiar with a plunger, you’ll know that the method of operation is not to keep a harmonious cycle, but to yank it aggressively in order to transmit a whole lot of impulse-like energy and forcefully release buildup or blockage in the pipes. My argument is that should we have two identical sinks with identical blockage and we’d manage to conduct an experiment where both plungers operate at identical frequency and amplitude, but that one plunger pumps in a harmonious cycle while the other does a pulse-like push pull, the latter would yield more successful results. Hence my conclusion is that despite the state being identical before and after, theoretically the amount of energy may be the same, there is a difference in how the energy is transferred depending on the curvature of the actuation on the plunger. Or the speaker cone. Though through air instead of water and air compress while water doesn’t. But still.

So the frequency of a repeated waveform and the shape of the waveform are not interchangeable. I’m sound the frequency carries the root tone, the shape carries the multiples. A perfect impulse (or other digitally generated waveforms) carry in theory an infinite amount of frequencies. Again, carry may be a misnomer depending on the discipline and of course the perfect is unobtainable so in practice the frequency spectrum is limited to one bandwidth and spectrum or another. Not that really had any bearing in our discussion.

Finally, I disagree with the argument of the engineering in headphones. Those limits are with respects of quality of sound reproduction. They are not a guarantee of hard limit of potential output and not intended to be. I don’t engineer speakers but it’s quite common paradigm in engineering in general that you benefit in quality and reliability should you accept a modest degree of unused overhead. Mistakes and bugs happen and it is especially vulnerable when it is reliant on hardware and software in the earpiece itself, as with my personal experience of faulty earbuds that emitted bursts of painful high frequency noise despite playback being of moderate volume. There are no intermediate steps of filtering, as with analogue gear, so should a faulty component cause a pop, it may well do so from the one extreme to the other.

I apologize for my frustration. I’ve been experiencing lately that I try to communicate one thing and the recepient keep projecting it into their own frame of reference and insist I’m talking of something that I’m not. I’m a bit touchy and I’m sorry about that.