As promised, here is the deep dive into Reverberation Time. It is long but I hope that it tells the story from start to finish and hopefully provides useful information beyond settling this argument.

**History Part I**
The origin of Reverberation Time is from Wallace Clement Sabine who around 1890 performed a ton of experiments in his basement to see how long it would take for sound to decay 1,000,000 times once it is shut off. Expressed in dB, we get 60 dB which happens to also be the sound level of a human. Sabine discovered that the decay time was proportional to volume (V) and inversely so to the total amount of absorption (Sa): RT60 = K * V / Sa (K is just a constant)

That kind of makes sense, no? You have more reverberations in a larger space than small. And an empty room like Ethan’s garage has more of it than one stuffed with furniture.

The Sabine formula was a godsend for early acousticians. Remember, this is a century before we have personal computers and nearly as long before we had pocket calculators. Anyone could perform the above math by hand and immediately get a sense of how a room would “sound” even prior to building it. People then performed surveys of performance halls and realized there is good correlation between how they sounded for different applications and RT60. It is not often that complex physics of a room with sound waves bouncing and absorbing becomes this simple to analyze.

**History Part II**
Decades later, Schroeder advanced our understanding of room reflections by introducing the concept of transition frequency below which, the room resonances/modes are separate and hence not random. He came up with a formula to determine this frequency which I showed in my last post. In reality there is no single frequency delineation (nature hates sudden changes) but a range above which we have the randomness we desire. For our home listening spaces, that ranges from 200 to 300 Hz typically.

The second thing he did was to come up with a reliable way to measure reverberation time. This is called the Schroeder Integral and is simply the sum of the square of measured decaying sound. I will show how this works in a minute.

**Measuring vs Predicting RT60**
So far we have talked about computing RT60 using the Sabine formula. I call that the predicted value of RT60. Its simplicity means that one can find cases where the prediction does not work as well. Let’s take the simple case of having a fully reverberant room meaning it has diffused reflections from all the hard walls. Now put an absorber in it. By definition the absorber will not bounce back some of the sound wave energy hitting it. As soon as you did that, your room is no longer fully reverberant. Put another way, the idea of a reverberant one does not exist in a realistic situation in big or small rooms!

Now think of a practical situation. You have a room with some furnishings in it. You add an absorber to it. The furnishings in your room caused your space to not have fully diffused reflections. That means the absorber experiences a different situation than it did in the reverberation chamber above. Sabine’s formula will mispredict how much of an effect that product has since its absorption coefficient was determined in a more reflective situation.

Instead of using the simple formula we can actually measure the decay of reflections in the room. Once there, we are free of many of the limitations of Sabine RT60. This is one of the reasons I am pushing back on all the theoretical objections against RT60. Often the text cited is old and implied in there is that the issues raised relate to Sabine formula, not

*in situ* version we use. Let’s see how this works.

**Measuring RT60 with Room EQ Wizard (REW)**
I am going to walk through how we can use REW to determine the proper value of RT60. If you have used REW, you know that it has a button for RT60. If you click on it, you may be puzzled that none of the graphs are named RT60. Instead, there are odd names such as EDT, T20, T30 and Topt. Let’s table that for a minute and learn a bit more about theory behind the measurement.

The concept for measuring reverberation is rather simple: excite the room with an impulse – a sharp spike of sound energy that has high/known amplitude and zero time – and then measure how long it takes for the reflections that are created as a result of it to die down by 60 dB. In practice we don’t use such impulses as they are hard to create in our rooms and can damage our gear. REW uses a modern technique called log swept sine which produces very good results without the need for loud test signals. But the end result is the same: we are measuring an “impulse” even though it sounds like a sine wave going from low to high frequency.

Let’s look at what happens when we hit the “Filtered IR” button. IR is short for Impulse Response (IR). This is what the output looks like:

The sharp peak at (roughly) zero time is our (computed) impulse. To the left we see our noise floor prior to our “impulse” playing. On the right we see us returning to the sane noise level after the reflections die off. Reverberations in a room drop off exponentially post the impulse going away. In the above graph the decay appears to be a straight line. The reason for that is that the vertical scale is in dB which is a log scale. Log is the inverse of an exponent so we wind up with a line.

Speaking of the line, there is one in black. That is the Schroeder integral. If this were an ideal reverberation chamber, we would have a perfectly straight line. We would then follow where it crosses the -60 dB point on the Y axis, and read our RT60 on the X axis which is in time. That is not the case here. Our line is not straight. We will fix this shortly.

Overlaid on the Schroder integral line is a blue line. If you look to the top right box, you see “Topt” selected. Other choices are T20 and T30. The latter two are standardized methods for finding the RT60 value from a less than perfect Schroeder integral. Instead of using the whole line to compute our RT60, we use a part of it and extrapolate from there. T20 uses the time it takes for reflections to die down between -5 and -25 (difference of 20 dB). Simply multiply that value by 3 and we get our RT60 time. T30 is similar and uses -5 to -35 and multiplies by 2. Both of these methods solve the problem of what to do if our noise floor is above -60 dB point. They also avoid looking at the start of the line which may be different. These are standardized computational methods per ISO 3382. As a result researchers use the same methods for consistency.

Topt is a much cleverer one in that it attempts to analyze the Integral and try to fit a line to it wherever it needs to start. Use Topt unless you have a reason not to (e.g. complying with ISO standard).

Looking at Topt line, we see that it pretty much tracks the Schroeder Integral except at the beginning of our impulse (between 0 and 50 milliseconds). There, we have a sharper drop than our Topt line represents and hence shorter reverberation time (the line would be steeper if we made it parallel to the early portion). That early part is called EDT (Early Decay Time). If you look at the box on the left, the RT time reflects that: Topt computation gives us an RT value of 0.659 seconds whereas EDT gives us 0.428.

What is the reason for that sharper early decline? The room that is being measured has carpeted floor. Once a sound wave hits that, it loses a lot of its power. Whatever bounces off the carpet is likely going to die soon. And once it does, it no longer contributes to the energy of the reflections that exist between the rest of the (reflective) surfaces such as drywall constructed walls. Another reason for the sharp drop is that in early stages we have strong reflections which push up the value of Schroeder Integral. Those go away after a while and we are left with our random/diffused reflections. As noted, all the standardized measurements of RT avoid the earlier part of the graph and hence, represent the “late” reflection timing of our room.

Back to our graph, REW provides a measure of how far off our RT measurement is from Schroeder integral with that “r” value (correlation coefficient). -1 is perfection meaning our single line matches the integral completely. Our Topt line is at -0.998 which is darn close with respect to our reflections past the initial 50 milliseconds or so.

So far we have looked the full spectrum RT. We know however that the low frequency modes likely are not following our rules. Let’s ask REW to show us RT60 for an octave of frequencies centered at 63 Hz:

We see a pretty chewed up line now since the reflection energy clearly is not random. We can try to fit a line to this but obviously there are a lot of deviations which REW notes with “r” values in orange. This means that the computation of RT for lower frequencies is probably not accurate.

Climbing up to 500 Hz cleans up the graph significantly:

With a nice line fit, you see why in research we used RT60 times for 500 Hz or higher. Let’s see what happens if we keep going up in frequency:

Even better. Now we are ready to go to the RT60 tab since you know what the different parameters mean. Here I have selected only Topt:

This is really a duplicate of our previous display except that the REW is doing the work for us of changing the frequency bands and plotting them as single values. We can easily read the mid-frequency RT60 times of 0.8 seconds. As a way of reference, the predicted RT60 using the Sabine formula for the same room is 0.66 seconds. Measured RT60 is higher due to one of the factor I mentioned: the absorption of material in the room is less than the ideal used in Sabine computation.

**What does it mean to you?**
A lot of objections were raised saying RT60 measurement is useless/meaningless in small rooms. With the knowledge at hand of what it is and how it is measured in a real small room, let’s see if that is the case.

Imagine you are playing a movie and actor says the word “hat.” We have three distinct parts to that with different loudness levels: “h,” a” and “t.” Let’s say it takes one second to pronounce “hat.” That means each part of it roughly takes 1/3 of a second or ~0.3 seconds. In our sample room we had a reverberation time of 0.8 seconds. This means that the pronunciation of “h” lasts another 0.8 seconds after it stops. That 0.8 seconds then overlaps the rest of the word. That may make it harder to hear the softer (in level) parts of that word. We may think the person said “had” instead of "hat." If we shortened our reverberation time to say, 0.2 seconds, the chances of that happening becomes much smaller and intelligibility improves.

Note that you don’t want to go too far here. The reflections help make the direct sound louder and hence easier to understand. Think of trying to talk to someone far away outside. It takes more energy than being indoor, right? Now you see why we have a lower bound for RT 60 values. The early reflections can be useful and we want to preserve them. But have the later ones die fast.

So as you see, RT60 is not useless at all. If we know what we are doing and measuring, we can extract useful data from it in order to determine if our room is too naked/live or alternatively over treated and too dead. Yes, with experience you too can determine the same by eye. Ethan did in his garage. And I could too without him posting the recording. That doesn’t invalidate RT60. It just says that our ears and experience can show the same. Indeed, Sabine did all of his measurements using his ears just the same!

If someone wants to challenge all of this, I hope they post measurements and data demonstrating their case.