Click here to purchase the entire book in PDF format. Reverberation If the walls were perfect reflectors and there was no such thing as sound absorption in air, this series of more and more reflections would continue forever. However, there is a little energy in the sound wave lost in the air, and in the wall, so eventually, the reflections get quieter and quieter as they reach a higher and higher order until eventually, there is nothing. Let's say that your sound source is a person clapping their hands once - a sound with a very fast attack and decay. The first thing you hear is the direct sound, then the early reflections. These are probably separated enough in time and space that your brain can interpret them as separate events. Be careful about what I mean by this previous sentence. I do not necessarily mean that you will hear the direct and earlier reflections as separate hand claps (although if the room is big enough you might...) Instead, I mean that your brain uses these discrete components in the sound that arrives at the listening position to determine a bunch of information about the sound source and the room. We'll talk about that more later. If we consider higher and higher orders of reflections, then we get more and more reflections per second as time goes by. For example, in our rectangular, two-dimensional room, there are 4 first-order reflections, 8 second-order reflections, 12 third-order reflections and so on and so on. These will pile up on each other very quickly and just become a complete mess of sound that apparently comes from almost everywhere all at the same time (actually, you will start to approach a diffuse field situation). When the reflections get very dense, we typically call the collection of all of them reverberation or reverb. Essentially, reveberation is what you have when there are too many reflections to think about. So, instead of trying to calculate every single reflection coming in from every direction at every time, we just give up and start talking about the statistical properties of the room's acoustics. So, you won't hear about a 57th order reflection coming in a a predicted time. Instead, you'll hear about the probability of a reflection coming from a certain direction at a given time. (This is sort of the same as trying to predict the weather. Nobody will tell you that it will definitely rain tomorrow starting at 2:34 in the afternoon. Instead, they'll say that there is a 70% chance of rain. Hiding behind statistics helps you to avoid being incorrect...) One immediately obvious thing about reverberation in a real room is that it takes a little while for it to die away or decay. So then the question is, how do we measure the reveberation time? Well, typically we have to oversimplify everything we do in audio, so one way to oversimplify this measurement is to just worry about one frequency. What we'll do is to get a loudspeaker that's emitting a sine tone with a constant level - therefore, just a single frequency. Also, we'll put a microphone somewhere in the room and look at its output level on a decibel scale. If we leave the speaker on for a while, the sound pressure level at the microphone will stabilize and stay constant. Then we turn off the sine wave, and the revebreration will decay down to nothing. Interestingly, if the room is behaving according to theory, if we plot the output of the microphone over time on a decibel scale, then the decay of the reverberation will be a straight line as is shown in Figure 3.79. Figure 3.79: Sound pressure level vs. time for a single sine wave in a room. The sine wave was turned on once upon a time - long ago enough that the SPL in the room has stabilized at the microphone's position. Note that, when the tone is turned off, the decay in the room is linear (a straight line) on a decibel scale. The amount of time it takes the reverberation to decay a total of 60 decibels is what we call the reverberation time of the room, abbreviated $RT_{60}$.