Originally Posted by bossobass
The effects of RR&T don't change at some magic frequency. They are the driver of the final FR in-room across the subwoofer bandwidth, assuming a minimum performance from the subwoofer in the first place.
Totally agreed: wave physics applies to all frequencies equally.
However, the result of the wave equation is different between short wavelengths and long wavelengths for a given sized room. There is no shortage of acoustics texts talking about this behavior. One of the advantages to splitting it up is it becomes easier to solve the wave equation by making different assumptions. Sure, any assumption is a deviation from the exact calculated result from the actual measured behavior, but we can quantity the worst case magnitude of that error and know that we're sufficient for any real application.
At the very lowest frequencies, below the modal region, the reflections effectively stay in phase with the direct sound. This has two distinct effects:
1) The listener experiences multiple acoustic sources (the reflections) summing together at the listening position
2) The subwoofer sees a larger acoustic load: this is really the same effect as horn loading. For the forward motion of the driver, the reflections from the room cause a larger pressure to exist in front of the driver, which in turns allows the driver to push even more air. Same thing happens in the reverse motion where it's trying to create a lower pressure, the negative pressure wave removes even more air molecules, and thus the woofer pulls to an even lower pressure. Basically, the subwoofer becomes more efficient. Eventually, this behavior gets capped at the point where the acoustic impedance is equal to the output impedance of the transducer - at which point you have the ideal case 50% efficiency. At this frequency, you no longer see any additional gain as you go lower in frequency. Then couple this with the lossy behavior of the walls and this is why you typically see a plateau type effect to the room gain. And if the walls are more lossy, then you'll see even less gains (which is why sometimes you don't get the ideal 12dB/octave).
If you want to solve the wave equation without making any assumptions, then go right ahead....you will find the exact same result within a calculable margin of error (which will be much less than the deviation any real room will impart).
Originally Posted by bossobass
Also equally astounding is the idea that when a boundary that has an Sd of 420,000 cm^2 is sent into sympathetic vibration at its resonant frequency, it will always cause a complete attenuation (the tech-term is suckout) of that frequency from the in-room response.
You have yet to show any measurement where a large boundary sympathetic vibration has increased the amount of energy in the room.
Here's what the electrical circuit for a band-stop filter looks like:
At really low frequencies, the impedance of the LC section approaches an open-circuit because of the capacitor. At really high frequencies, the inductor makes it an open-circuit. At some frequency inbetween, there is a minimum impedance associated with the resonant frequency. It is at this frequency that it creates the acoustic short circuit. For a voltage source (the pressure wave), it's impossible to get a higher voltage than an open-circuit.
Below the modal region of the room, the acoustic source output impedance is no longer reactive (which would be the sum of the driver + all the other reflections). Therefore it is impossible for a band-stop filter to create more amplitude than comes into the node. The pressurization region is the only caveat I ever gave to the sympathetic resonances - and that's because most building resonances fall below the modal region.
Also, nowhere did anyone say that this resonance creates a huge -infinity suckout in the frequency response at the listening position. If you see -6dB at the listening position from a wall resonance, then that means half of the energy arriving at the listening position was probably being reflected off that wall. In other words, it essentially becomes the absence of a boundary - so no pressurization is happening at the surface of that wall at that frequency.
Inside the modal region, or near the reactive output impedance of the acoustic source, it is possible for resonances to have +/- effects, but there is still a net energy loss in the room. This is the fundamental basis of a Helmholtz resonator. Surely you aren't suggesting that I'm unaware of their positive effects in the modal region? Any graph that you might claim showing an increase, it is required that the acoustic impedance on the vibrating wall be reactive.
Anyways, none of the measurements here contradict any of these theories. Any extent to which you think they do, I would kindly suggest that you are mis-applying the theory. But hey, you're not formally trained, nor an engineer, and you certainly don't make your living based on how well you apply these theories - so I honestly expect no less and it's no discredit to the hobbyist. However, if you want to provide an actual rebuttal that offers any meaning, then let's bust out the wave equations and crank through the calculus. This stuff is actually one of the easier applications to solve the wave equations with. Or if you're afraid of the math, then let's stick to measurements showing actual causation instead of correlation - that would start with an actual rectangular room.