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)?
A few observations.
First - if you record sound for a short time, the bandwidth of the sample will result in a smearing of the peaks. This only really matters if the sample is very short - with a 1 second sample you would have 1 Hz resolution, but if you sample for 0.01 second, the bandwidth is 100 Hz.
Second, you are using a scale that is quite compressed in the region of interest. That again makes me wonder whether you have not set up your sampling to be optimal for the frequencies of interest.
I have used a cheap iPhone app in the past to record sounds (Signal Spy - I am not connected to the product) and get an idea of their spectral content. I just played a simple scale on my guitar, and got the following (time along the horizontal axis, frequency vertical, intensity shows what frequencies are detected):
I have the feeling there's a problem with the labels on the logarithmic scale, but you can clearly see the fundamental and its harmonics; they are much better resolved than in your case.
This means that either your frequency is not constant, or your recording settings are very much not optimal for the task. Perhaps you can comment on the settings you used, and we can figure out how to get similar results for you. You used the words "a short region of the recording with minimal resonance was used..." - I wonder if your recording window was too short. I also wonder what windowing technique you used. When you do frequency analysis, you don't simply do the Fourier Transform of a snippet of sound - because if you do, you will generate a bunch of frequency content due to the way the signal "cuts off" at the start and end of the recording. Instead you need to apply an apodizing window (Hamming or Hanning window, usually) to get rid of extraneous peaks, and get cleaner frequency peaks.
If you have a pitch generator, the most accurate thing you could do would be to play the known pitch and slowly ramp it until the guitar string started to resonate. That works very well... as the resonance width is quite narrow. You would be able to determine the frequency within a fraction of a Hz (assuming your pitch generator produces enough output - perhaps you play it through a microphone and amplifier into a decent speaker).
Best Answer
Multiply your values my some number less than 1.0. That will "move all the values closer to zero". But remember that the human hearing system is logarithmic, not linear. And "volume" is a psycho-physical phenomenon that is hard to quantify, and varies from person to person.
Reducing your values by a factor of two will not reduce the perceived volume by a factor of two. Rule of thumb: it takes a reduction of 6 - 10 dB in intensity to reduce perceived volume by a factor of two. 6 dB is a factor of 4, 10 dB is a factor of 10. Let's take the high end: 10 dB. To reduce the loudness by a factor of 2, you might have to multiply your values by 0.1. To reduce the loudness by a factor of 4, you might have to multiply by 0.01.
If you are not aware of these things, you might not be reducing your values nearly enough. Experiment my multiplying your values by factors in the 0.1 - 0.2 ballpark. Don't be afraid to to use much smaller values.
update after comment
Eliminating distortion: It depends on the system you use to realize your sound wave (your audio system), the nature of the sound wave (does it have a lot of sharp peaks) and your tolerance for distortion. Eliminating all distortion is impossible, as no reproduction system is perfect. You can eliminate clipping/saturation by reducing total volume, but if there is any small peak at all your volume might be very very low. Allowing a small, inaudible amount of distortion would help. Sometimes dynamic compression is used to reduce audible distortion while keeping the volume reasonably high.
Harmonic distortion occurs before the primary effects of clipping are audible. Can you tolerate that?
Reproduction systems always change the amplitude and phase of each frequency component. That's an unavoidable distortion. If you think you want to avoid that, you are sunk.
The fact that you have a digitized version of the waveform is a distortion.
We really need more context. What are you trying to do?