Sorry for the late response guys. Been travelling with non-stop meetings for the last few days.
Originally Posted by GIK Acoustics
To state my point more clearly, I'll quote from the same book in Chapter 8, Small Room Acoustics:
My point (to clarify) is not to prove one wrong about the reverb definition (I simply don't care the term one uses, I use the terms interchangeably depending on who I'm talking to), but to simply state: the RT60 calculation is useless in a small room.
You have not give us any independent data why you believe that. So let's go to the horse's mouth and examine how strong Davis' proof points are that such a measurement is "meaningless" as he states.
The section you are quoting is less than a page long and is titled, “Small Room Reverberation Times”. I will address the theory points he puts forward in another reply but for now, let’s examine the back up he puts forward in the form of a quote from Dr. Schultz’s 1963
AES Journal paper, ”Problems in the Measurement of Reverberation Time.”
Unfortunately Davis' only shows you a snippet instead of the full context of that (very good) paper. I will remedy that here.
As the title indicates, the paper is about what can go wrong in measuring reverberation times using various techniques. He starts with this case study:Consider the curves shown in Fig. I, which purport to display the reverberation time of a small rectangular room plotted as a function of frequency. The upper curve gives the reverberation time when the room is completely bare. It shows an extreme variation of reverberation time with frequency. The lower curves were obtained by adding progressively more sound absorptive material to the room.”
“CPS” is cycles per second or as we commonly call it, Hertz. So the chart’s horizontal axis ranges from 10 Hz to 10,000 Hz. He goes on to explain what is wrong:”What, then, is the trouble with these curves? Surprisingly, there appear to be at least three methods of measurement which would give this kind of wrong answer! The first of these consists of measuring the reverberation in the room indirectly by means of a standard acoustical source of known power output. This method works fairly well in a large room in which a great number of the room modes crowd together and overlap in any reasonably small frequency band.”
So the key to the measurement being correct is having many modes overlapping. Where do we run afoul of this in our small rooms? He explains it:
“In a large room, if one has a large sound source whose power output is known, one can determine the total amount of absorption in the room by measuring the average pressure throughout the room. This total absorption can then be used to calculate the reverberation time from the Sabine formula. This method fails badly in a small room, however where, a large part of the spectrum of interest lies in a frequency range where the resonant modes of the room do not overlap but may be isolated , as shown in Fig. 1 (individual resonance peaks are identified with their corresponding mode numbers).
In this case the microphone, instead of responding as a random sound field (as required for the validity of the theory on which these methods depend), will delineate a transfer function of the room. This is a curve which gives response in terms of modal frequencies, but only a little about the absorption on the boundaries.
It does not provide a valid measurement for the reverberation time in the room however.”
The above is the only part of the paper quoted in Davis’ book except that he omits the sections in bold. When we add them in and focus on key sections I have highlighted in red, we realize that this is not at all supportive of the broad assertion made by Davis and you repeating the same. Dr. Schultz is focused on the modal region below 100 to 200 Hz and saying that we do not have many modes in small rooms so we better be careful in applying simple RT60 formulas.
What does this mean in English? Modes create peaks and dips in the room response at certain frequencies which we can theoretically predict using modeling. Let’s use Ethan’s tool and apply it to a typical home listening space which in acoustic domain is considered “small:”
We see that at frequencies less than 100 Hz, the modes are indeed pretty sparse. To wit, below 50 Hz with have just one at ~28 Hz. Let’s compare this to a much larger room:
Quite a different picture emerges as we now get lots of room modes in the same low frequency area below 100-200 Hz. I want to reserve the theory of why we need many modes for the next post but for now, let’s accept what we want is what Dr. Schultz says: many modes for the reverberation times to be more accurate.
One “solution” to getting more modes is to do per above which is to have a much larger room. But there is another: move up in frequencies. Look at the density of modes on the right edge of our small room: it is starting to have lots of modes packed together much like what the larger room has at lower frequencies. Translating, if the RT60 measurements are accurate to a low frequency in large room, they are accurate just the same for small room except that we need to move up in frequencies.
If you search for my posts and countless peer reviewed literature in Journal of ASA and AES which use RT60 measurements in small spaces, the above is precisely the recommended practicethey do: the RT60 measurements are for “mid-frequencies.”
I use 500 to 1000 Hz; others use the same or go up to 3 KHz or so. RT60 is not provided as a measure to evaluate modal (e.g. subwoofer) region. There we use frequency response to reveal the impact of the modes. Therefore, our practice and that of countless other researchers is very much in compliance with the concern that Dr. Schultz shares.
So the claim of the measurement being useless is not supported by the citation in Davis’ paper. He creates a scenario (using it in modal frequencies) and then shoots it down.
To be fair, at mid frequencies our modal distribution in a small room has not yet fully achieved Poisson distribution (discretely random in space and time but with a known long term average). I will address why this is not an impediment to analysis of our small spaces in the next post.
As if he knows that the Dr. Schultz point only applies to modal low frequency region, Davis’ next immediate section, 8.4 titled “Small Room Resonances” is a discussion of room modes!
Believe it or not the best part of this answer is yet to come!
In this section, he provides this graph:
Seems familiar, no? It is the exact same measurement as Dr. Schultz used sans the repeat sin of saying where it came from!
This is the text that goes with that graph:”In Fig. 8-4, the effect of “undamped” modes are plotted, as a decay time, for small broadcast studio. The damping is provided by diaphragmatic absorption at the lower frequencies. “
Get it? He uses the very graph Dr. Schultz used to say represents wrong information, renames it to “decay time” and claims it now holds valid data!!!
How could a measurement go from meaningless to so useful by just changing the term that way? Note how the graph still says Reverberation time!
It gets more interesting. Dr. Schultz’s paper was published in 1963. The measurement above must have been performed prior to 1963 or else, Dr. Schultz could not have quoted it. The first revision of Don Davis’s book which by the way did not have professor Patronis involved came out in 1987. How is it that someone writing a text on acoustics has nothing more current and appropriate to use to demonstrate room modes than a measurement from some 25 years back??? And one that completely torpedoes his case just half a page back??? Your guess is as good as mine but I am afraid it indicates that maybe Davis did not read the Dr. Schultz paper either.
I don’t want to take anything away from Don Davis’ reputation or work. But let’s all agree that this is not how we go backing strong assertions. Take a look at the Dr. Toole coverage of the same topic and it goes on for tens of pages, encompassing research paper and data after research paper and more data. You can go read any of the original research as I have done and you will have a heck of a hard time invalidating the conclusions he draws from them. Everything in Dr. Toole’s case is referenced properly so that people can double check if they want. Not so here sadly.Summary
Davis makes a very bold claim that RT60 measurement is meaningless. Folks proceed to repeat the same all of the Internet and hammer into people as gospel. Yet just one level of digging shows that the backup data Davis uses refers to not using RT60 for low frequency analysis. That is a non-point since the proper use of RT60 is for analysis of mid-frequencies, not modal low frequencies. Worse yet, Davis turns around uses what is said to be faulty data as his proof point for something else by just swapping names! I get believing in what experts tell us but come on now. People in the industry should at least dig one level further and read research references before believing.
As I noted in part two of this post (in the next few days) I will address the theory points Davis’ sites for those who really want to know “how the sausage is made.”