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)?
Do low frequencies carry farther than high frequencies? Yes. The reason has to do with what's stopping the sound. If it weren't for attenuation (absorption) sound would follow an inverse square law.
Remember, sound is a pressure wave vibration of molecules. Whenever you give molecules a "push" you're going to lose some energy to heat. Because of this, sound is lost to heating of the medium it is propagating through. The attenuation of sound waves is frequency dependent in most materials. See Wikipedia for the technical details and formulas of acoustic attenuation.
Here is a graph of the attenuation of sound at difference frequencies (accounting for atmospheric pressure and humidity):
As you can see, low frequencies are not absorbed as well. This means low frequencies will travel farther. That graph comes from this extremely detailed article on outdoor sound propagation.
Another effect that affects sound propagation, especially through walls, headphones, and other relative hard surfaces is reflection. Reflection is also frequency dependent. High frequencies are better reflected whereas low frequencies are able to pass through the barrier:
This is and frequency-based attenuation are why low-frequency sounds are much easier to hear through walls than high frequency ones.
Frequency Loudness in Headphones:
The above description apply to sounds that travel either through long distances or are otherwise highly attenuated. Headphones start off at such low intensities already they don't travel long enough distances for attenuation to be a dominate factor. Instead, the frequency response curve of the human ear plays a big role in perceived loudness.
The curves that show human hearing frequency response are called Fletcher–Munson curves:
The red lines are the modern ISO 226:2003 data. All the sound along a curve is of "equal loudness" but as you can see, low frequencies must be much more intense to sound equally as loud as higher frequency sounds. Even if the low frequencies are reaching your ear, it's harder for you to hear them.
Headphone sound is doubly compounded by the difficulty of making headphones with good low-frequency response. With loudspeakers you can split the job of producing frequencies among a subwoofer, a midrange speaker, and a tweeter. For low frequencies subwoofers are large and have a resonating chamber which simply isn't an option with headphones that must produce a large range of sound frequencies in a small space. Even a good pair of headphones like Sennheiser HD-650 struggle with lower frequencies:
So if it sounds like high frequencies travel farther with headphones, it's because headphones are poor at producing low frequencies and your ear is poor at picking them up.
Best Answer
Several things to consider: The speed of sound is much higher in water than in air. Just how much depends on a lot of factors. On http://www.waterencyclopedia.com/Re-St/Sound-Transmission-in-the-Ocean.html it says:
So the type, and quality of water can make a big difference - note particularly the bit on 'scatter, absorb, or reflect', and thosw are likely frequency dependent to boot.
Next, while you can buy underwater speakers, you generally need to massage the waveform so you hear it 'properly' underwater (i.e. as if you were in air). My kids' swim team has such a rig, which is much better than trying to listen to Iron Butterfly through an uncorrected audio system in college...