why do textbooks never mention this?
Because in order to travel at supersonic speeds, human beings must be enclosed in a rigid metal tube of some sort. Also, these metal tubes they ride in at those speeds generally tend to be insulated against noise from the outside.
As for trying to place some sort of microphone outside said metal tube, the propulsion system would risk drowning out any atmospherically transmitted noise (i.e. noise can be transmitted through the body of the structure).
Now, if you run the math, it still doesn't work quite like hearing it backwards (see the comment by eudoxos). Although you would encounter the soundwaves in "reverse" order, the shockwaves around you would disrupt anything around you as to make the notion of noise from them irrelevant.
Please note that the following is all conjectural. I only volunteer it due to the lack of other responses after numerous days, the coolness of the question, and the probably lack of people/references who are explicitly experienced with this specific topic.
Basic Picture
As a general relation, I'm sure one can correlate the sound-volume with the total energy being dissipated --- but the noise produced is going to be a (virtually) negligible fraction of that total energy (in general, sound caries very little energy1).
To zeroth order, I think it's safe to assume the waterfall produces white-noise, but obviously that needs to be modified to be more accurate (i.e. probably pink/brown to first order). Also, by considering the transition from a small/gradual slope, to an actual waterfall, I can convince myself that there is definitely dependence on the height of the fall in addition to the water-volume2.
How would height effect the spectrum?
Generally power-spectra exhibit high and low energy power-law (like) cutoffs, and I would expect the same thing in this case. In the low-frequency regime, if you start with a smooth flow before the waterfall, there isn't anything to source perturbations larger than the physical-size scale of the waterfall itself. So, I'd expect a low-energy cutoff at a wavelength comparable to the waterfall height. In other words, the taller the waterfall, the lower the rumble.
There also has to be a high energy cutoff, if for no other reason, to avoid an ultraviolet catastrophe/divergence. But physically, what would cause it? Presumably the smallest scale (highest frequency) perturbations come from flow turbulence3, and thus would be determined primarily by the viscosity and dissipation of the fluid4. Generally such a spectrum falls off like the wavenumber (frequency) to the -5/3 power. But note that this high-frequency cutoff wouldn't seem to change from waterfall to waterfall.
Overall, I'm suggesting (read: conjecturing) the following:
- Low-frequency exponential or power-law cutoff at wavelengths comparable to the height of the waterfall.
- High-frequency power-law cutoff from a kolmogorov turbulence spectrum, at a wavelength comparable to the viscous length-scale.
- These regimes would be connected by a pink/brown-noise power-law.
- The amplitude of the sound is directly proportional to some product of the flow-rate and waterfall height (I'd guess the former-term would dominate).
E.g.: The following power spectrum (power vs. frequency - both in arbitrary units).
The Answer
I'm sure information can be obtained from the sound. In particular, estimates of its height/size, flow-rate, and distance5. I'm also sure this would be quite difficult in practice and, for most purposes, just listening and guessing would probably be as accurate as any quantitative analysis ;)
Additional consideration?
I suppose its possible waterdrop(let)s could source additional sound at scales comparable to their own size. That would be pretty cool, but I have no idea how to estimate/guess if that's important or not. Probably they would only contribute to sound at wavelengths comparable to their size (and thus constrained by the max/min water-drop sizes6...).
Water, especially in a mist/spray, can be very effective at damping sound (which they used to use for the space-shuttle). I'd assume that this would have a significant effect on the resulting sound for heights/flow-volumes at which a mist/spray is produced.
The acoustic properties of the landscape might also be important, i.e. whether the landscape is open (with the waterfall drop-off being like a step-function) or closed (like the drop-off being at the end of a u-shaped valley, etc).
Finally, the additoinally surfaces involved might be important to consider: e.g. rocks, the surface of the waterfall drop-off, sand near the waterfall base, etc etc.
Endnotes
1: Consider how much sound a 60 Watt amp produces, and assume maybe a 10% efficiency (probably optimistic). That's loud, and carrying a small amount of power compared to what a comparable-loudness waterfall is carrying. The vast-majority of waterfall energy will end up as heat, turbulence, and bulk-motion.
2: I'd also guess that height/volume blend after some saturation point (i.e. 1000 m3/min at 20m height is about the same as 500 m3/min at 40m height)... but lets ignore that for now.
3: Turbulence tends to transfer energy from large-scales to small-scales.
See: http://en.wikipedia.org/wiki/Turbulence
4: Figuring out the actual relation for the smallest size-scale of turbulence is both over my head and, I think, outside the scale of this 'answer'. But it involves things like the Kolmogorov spectrum, and associated length scale.
5: Distance could be estimates based on a combination of the spectrum and volume level - to disentangle the degeneracy between sound-volume and distance.
6: Perhaps the minimum droplet size is determined by it behaving ballistically (instead of forming a mist)?
Best Answer
Yes, but not through the air. The sound is largely generated internally to the fuselage of the plane. While sitting on the deck ready for takeoff, then the engine would likely be much louder but the cockpits are often surrounded by heavy materials reducing sound transmission anyways. It's just that fighter jet engines are so obnoxiously loud, e.g., see notes about this at: https://physics.stackexchange.com/a/281767/59023.
Your second questions is likely closer to the truth than the former. The reason being that shock waves cause an abrupt change in the index of refraction for light and for compressive sound waves in a medium. So much so that sound waves can actually reflect off of the shock wave (e.g., sometimes shock waves reflect off of each other). Most linear sound waves that start outside of and in front of a supersonic jet would likely be reflected and destroyed. That is, immediately after reflection the wave would be overtaken by the shock since the sound wave propagates only at the speed of sound whereas the shock speed is defined by the piston/driver (i.e., supersonic jet here) speed.
Regardless of this, one would need a rather intense sound to actually be heard. That is, suppose we ignore the issues with crossing the shock barrier. The sound would need a greater intensity than that of the jet, which is not insignificant as I noted above. Further, the sound would need to be extremely loud to be heard inside the pilots helmet which is intentionally designed to reduce outside noises for communication purposes. My guess is that something like a missle explosion may be heard, but unfortunately it may have to be close enough to cause damage to the craft.
I will pester a colleague of mine that used to be an air force pilot to get a more definitive answer.
Update
I spoke with my air force buddy and he said a few things that kind of confirmed what I had originally thought. So most of the noise in the cockpit is due to the engines and it is primarily transmitted through the solid body of the fuselage. The cockpit is intentionally designed to reduce noise from outside sources. Further, the helmet has additional noise reduction methods implemented to allow the pilot to mostly hear comms and not much else (besides the vibrations of the engine, of course).
In general, shock waves reflect off of each other so explosions ahead of a supersonic jet might be felt but likely not heard unless they are extreme (in which case the integrity of the jet may be more of a concern than whether the pilot can hear the external noise source).