Originally Posted by audiophilesavant
Ethan's 37.75" by 22.5" by 14.5" empty, glass-lined box has an RT60 of approximately 0.3, which according to you is just about right, or perhaps slightly on the dead side. Is Ethan's RT60 measurement providing useful information?
Thank you for your question. Before I answer it, I hope you join me in commending Ethan for taking the time to set up such elaborate fixtures to test the notions posted on the Internet. I always give him kudos for having an inquisitive mind that wants to prove to himself that his understanding of the science is correct.
Back to your question, the breadcrumbs are in this thread to answer that. Let’s review them again as a refresher.
The box, and let’s be clear that it is a small one given those dimension in inches, has very small amount of volume:
By my math it is only 6.5 cubic feet. In one of my earlier posts (http://www.avsforum.com/t/1453370/do-bass-traps-produce-noticeable-audible-difference/90#post_23008908
) I talked about the Schroeder transition frequency. This is the frequency below which the modes are too separate making our room response more location specific. For our typical home listening spaces, that frequency is usually in the 200 to 300 Hz region so you almost don’t need to do the math there. This little box however is far smaller than a real room so let’s do the math for it:
Fc = 11885*SQRT(RT60/V); let’s plug 6.5 in there for Volume and stated 0.3 RT60 time. That gives us the Transition Frequency of 2,535 Hz. Alas, the Schroeder’s formula was arrived at empirically (working backwards from measurements) and never tested against such a little box. The way we compensate for that is to instead think of this as somewhere in the middle of a much wider range of frequencies (much like I did in my “200 to 300 Hz” statement above). I don’t have direct data on how wide we need to make it in this small space but I think it is safe to say that the transition region could easily range from 2000 Hz to 3000 Hz. Let’s park this for a moment.
The idea behind a target reverberation time is to balance two needs: 1) speech intelligibility which is important in both movies (dialog) and music (singer) and 2) nice feeling of space we get from room reverberations. These two factors kind of fight against each other to some extent as ideally we like to have both. That is why we have a range specified of 0.2 to 0.5 rather than a single number. This range however is not computed but based on industry's collective experience of what the value should be based on countless in field experiences in home listening spaces. That experience has been formed from typical home spaces, not a small box like this or an auditorium. The latter actually has its own set of recommended RT numbers which are larger than this. There has been no interest in characterizing how good speech sounds in such a little box so hence, there is not a recommended range for it.
Ignoring the above fact for a moment, we can walk through the analysis anyway and see where that gets us. We have an RT60 time of 0.3. Numerically 0.3 is in that range but there is a problem: our transition frequency has shot up by a factor or 10 over a typical room. Recall that I said in the research and industry our target frequency of interest is 500 Hz although that is often stretched to 1K to 2K Hz. One of the reasons for this was the fact that we would be free of the modal issues (large response variations) below transition frequencies of 200 to 300 Hz of our rooms. We immediately see a problem here. We can’t use RT60 @ 500 Hz since a) Ethan did not test that frequency and b) it would be below the transition frequency.
You might be asking why we don’t look at higher frequencies since they would be above transition range for this box and we do have the data for that. That does not work either. Look at the spectrum of speech in this sample spectrogram as the person pronounces “Rice University:”
This is a nice visualization of the problem with speech intelligibility and late reflections. It is clear from the time graph at the bottom that the intensity of speech changes every 0.2 seconds or so in English language (it may be faster or slower in other languages). The larger colorful graph shows the frequency spectrum at any moment and color coding of the energy/strength. Red means very strong, blue means very week. It is pretty clear that the bulk of vocal energy is below 2,000 Hz. It therefore matters not what higher frequencies are doing as they don’t have a lot of energy at the start. Evaluating RT60 times well into Khz region therefore is not material to this analysis. It is like trying to figure out engine idling problems in a car with a tachometer that starts at 2000 RPM.
Fortunately there are no applications for dollhouse sized home theaters or listening spaces so there will be no riots in the streets that we can’t perform such an analysis.
BTW, there is a small listening space of high interest to us: cars. Their smaller volume means that the modal region climbs up to 500 Hz or even higher. Getting smooth response is hard in our homes below 100 Hz. Now imaging that problem multiplied and moves up in frequency, now impinging on low range of even voices! Inversely, as I mentioned before, larger performance spaces have much lower transition frequencies usually below 20 Hz, which eliminates the modal concerns altogether. These are the factors that are important as we look at “small” and “large room” acoustics, not some worry about RT60 measurement being wrong.
Back to Ethan’s box and experiment, he was simply comparing two surface materials against each other: MDF vs. glass. We know glass is smoother than MDF resulting in theoretically less absorption in higher frequencies. Less absorption means higher reverberation time (what doesn’t get absorbed, gets reflected). Since the measured RT60 time tracked this difference correctly, we have yet another validation point that this measure is accurate! Here is his RT measurement:
If RT60 measurements were useless then we should have arrived at random data and not have experiment after experiment, showing the correlation with amount of absorption introduced in the space.
BTW, the whole argument is circular anyway. You can’t prove RT60 measurement is meaningless using RT60 measurement itself! You have to have an independent metric that is believed to be true that shows RT60 to be wrong. This is how we showed error in the *computed* RT60. We trusted RT60 and showed that the formula must be in error.