Assignment 6: Calculations Do the following on paper, scan or photograph your work, and submit it. You have a room that is 4 m long, 7 m wide, and has a ceiling height of 3 m. The floor is hardwood

Sabine Equation

Reverberation time can also be calculated if we know the volume and total absorption of a room. The most common method of calculation is known as the sabine equation, named for its discoverer, Wallace Clement Sabine. Sabine developed this relationship between volume, absorption, and reverberation time empirically by measuring the T60 for various amounts of absorption in a room. Because it is empirical, the units do not work out the way you'd expect. The sabine equation is:

V is the volume of the room in m3 and A is the total absorption in metric sabins.

One metric sabin is equivalent to 1 m2 of 100% absorptive material (a = 1). The original use of the term sabin to describe absorption was in English units, so we use the term metric sabin to distinguish from the standard sabin.

The total absorption, A, is calculated using this equation:

S is the surface area in m2 of a surface in the room. The Greek letter sigma is used in mathematics to designate a summation. That simply means that we will multiply the surface area and absorption coefficient for each surface in the room (thus finding the equivalent absorption of each surface) and add them to find A, the total for all of the surfaces in the room. Another way to look this equation is:

where n is the total number of surfaces in the room.

An example should make this more clear.

Here is the room that we looked at earlier when we calculated mean free path. It now has absorption coefficients indicated for each of the surfaces.

The sketch also indicates that the 1000 Hz octave band is represented. These coefficients would likely be quite different for other bands.

To find the total absorption, we will first find the absorption of each surface by multiplying its surface area (S) by its absorption coefficient. We can then add these totals together to get A.

Doing this in a table may make it easier to visualize the steps:

We know now that A = 33 metric sabins. Let's find the volume of the space:

3 m x 5 m x 2.5 m = 37.5 m3

Now we can plug these values into the sabine equation to find the 1000-Hz reverberation time: