There is a simple formula--not perfectly accurate--that predicts the reverb time of an enclosure. The equation was first derived by Sabine one of the pioneers of auditorium acoustics. The equation states that the reverb time in seconds is given by the equation:

RT = -.161 ^V / _A 

where RT stands for the reverb time in seconds, V is the volume of the enclosure in cubic meters, and A is the room absorption in square meters that we learned how to calculate in the previous web page. This is called the metric version of Sabine's equation. If the areas and volumes are in feet rather than meters then the coefficient 0.161 is replaced by 0.049.

Before we look at some examples of using the reverb time equation lets examine it to see if it makes sense. First, note that the reverb time is proportional to the volume of the room; thus, a large room implies a long reverb time. This observation agrees well with our intuition. You might ask why the large room volume leads to a long reverb time. Remember that the energy is absorbed by repeated reflections from the room walls. In a large room the time between collisions with the walls is longer just because the distance between walls is larger, thus it takes the energy takes longer to dissipate leading to a longer reverb time.

Similarly, if the absorption, A, is large, energy is dissipated more quickly and the reverb time is short. Dividing by the absorption means that large A corresponds to shorter RT. Cool.

Now this equation for reverb time is only an approximation, although a pretty good one for most practical situations. Let's examine a situation in which it does not work. Imagine the walls are perfectly absorbing--what is the reverb time? I hope you thought a moment and then answered "zero"! Perfectly absorbing walls imply no reflections and the sound dies instantly after the source cuts off. Now lets see what the equation predicts. The absorption A will equal the internal surface area of the walls (see Self Test question on the previous page!) and the volume is just V. A and V will be numbers and thus the equation predicts some value of RT that is not zero! To cure this problem there are many more sophisticated models, however, we will not look at them, our simple equation will suffice.

Here is an example of using the reverb time equation.

Example 1

Calculate the reverb time for the 7 m x 7 m x 7 m room described in Self Test 2, question 1 on the previous page.

We found that the absorption A = 91.14 m². The volume V = 7 x 7 x 7 m³= 343 m³. Thus the reverb time is given by RT=0.161*343/91.14 = 0.61 seconds.

Now you can try these self test examples. And then it's on to the QUIZ! GOOD LUCK.

Self Test

1. Calculate the reverb time at 500 Hz for the 12 m x 10 m x 5 m room described in the previous page Self Test 2, question 3.
2. Calculate the change in reverb time that occurs if suspended acoustic ceilings are installed in the room (see previous page Self Test 2, question 4).
3. A room with a volume of 1000 m³has a reverb time of 1.8 seconds. What is A?
4. For the room in the previous question, to what value would you have to increase A to reduce the reverb time to 1.4 seconds?

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