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

Reverberation Time

In the impulse response graphs, we observed that the decay of the reverberant tail is fairly linear, and that the slope of the decay could be described in terms of dB/octave. This slope is an excellent way to quantify reverberation. However, instead of using the slope itself, we use a metric called reverberation time.

Reverberation time is the time it would take for the reverberation to decay by 60 dB. It is abbreviated T60. Ideally, we would have at least 60 dB of decay, and could just look at the time that it took. However, we are often limited by the noise floor in the room—the noise that is always present from building mechanical systems, traffic, etc. The word "floor" reflects the fact that this noise marks the lower boundary of the range of amplitude that we are able to use for our measurement.

If we have less than 60 dB of decay before the signal goes below the noise floor, we can extrapolate using the slope. For example, if we could measure the time it takes to decay by 30 dB and simply double that time to find T60. This simplified plot shows a reverberant decay that begins at a sound pressure level of 100 dB at a time of 0.25 sec.

To find the T60, we simply look at the time it takes to decay by 60 dB. 100 dB - 60 dB = 40 dB, and the time at which the slope passes through 60 dB is 2.25 sec. 2.25 sec - 0.25 sec = 2.0 sec. So T60 = 2.0 sec.

In the example above, we have enough signal above the noise floor that we do not need to extrapolate to find the T60. In the example below, this isn't the case. Here, we only have about 40 dB of signal above the noise floor.

To find T60, we'll simply look at the time it takes for a decay of 30 dB and double it. Since it takes 0.75 seconds to decay by 30 dB, the T60 is 1.5 s.

Because of its frequency dependence, we have to measure reverberation in octave- or one-third-octave bands. This requires that the source of sound used contains all of the audible frequencies. An impulse works well for this, and is the most common source. A more traditional method involved playing random noise through a loudspeaker and cutting it off suddenly. The reverberant decay would be very similar to that which follows an impulse. We now have digital systems that can mathematically synthesize an impulse from other types of signals. We'll look more at these in a couple of weeks.