@ Mclerico

Go Bulls. I'm on CA.com instead of working on my Mech. E. thesis @ University of Houston
Your explanation is correct for the most part, but I'll clarify the designation between distortion and clipping.
Distortion is when unwanted harmonics appear. If you play a 100 Hz tone, and the amplifier may leak out a 200 Hz overtone. THD is a measure of how much junk gets added between the input and output.
Clipping is when the sine wave gets flattened, when the amplifier cant supply enough rail voltage. The flat top becomes a square wave, as clipping increases.
The same way a Fourier series can recreate a square wave using sine waves (the fundamental frequency plus the added overtones) ... so does the amplifier. You keep sending more power (area under the curve), but alot of this power is lost to heat, since the overtones are counteracting the fundamental cone movement. In the same way a sub will act when you wire dual voice coils opposingly. More input power without added cooling (convection). This is where the added heat comes from.
Summary:
Woofer death is usually due to overheating. Overheating is usually due to distortion created during clipping. Clipping is preventable... so don't be a dummy.
PS - I'm one of those poor souls who use Audiopipe amps. Ironically enough, I've abused them for a couple years of competition and World Finals. Now I'm using them in my SQ setup. When gains are set properly, 99% of class D amps will have indistinguishable SQ for sub-bass. Subwoofer distortion is not noticeable in modest quantities (<10%), so if you could stop polluting the thread with audiophile snobbery, the world would be a better place. Thanks.
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