The waterfall plots I know all show only the decay, not the rise. And the decay on the low frequencies is much longer than elsewhere.
Edit: here are typical examples from
Stereophile (Estelon Aura) and
Sound & Recording (Neumann KH310, sealed box):
Yes! It's math,
Fourier series:
The first four partial sums of the Fourier series for a square wave. As more harmonics are added, the partial sums converge to (become more and more like) the square wave.
Yes, and this leading edge of the rise consists of high frequencies. The spectrum of percussions is very wide and ranges from almost DC up to high frequencies.
See this example from
Wikipedia, which starts with a low frequency sinus (fundamental) with a slow rise, and then adds more and more harmonics with rising frequency. The more harmonic are added the steeper gets the rise:
If you have access to a sub then do this experiment: play percussive sounds with what you'd call a fast bass. Then disconnect the satellites and listen to the sub only, and tell me whether the percussion still sounds fast.