0.1 Reverberation in enclosed spaces

Reverberation

When sound is made in an enclosed space, echoes of the signal reflect of the room’s surfaces and form a reverberated signal , a superposition of the signal generated and delayed versions of itself with amplitude decay. These reverberations make listening unpleasant and can sometimes make a presentation unintelligible. The OEDK classroom suffers greatly from reverberations which are distracting when listening to recordings of presentations.

Two room impulse responses

Reverberation time

The reverberation time of a room is the time it takes for sound to decay by 60 decibels. The reverberation time of a room can be approximated by the Sabine Equation :

where $c$ is a constant relating to the speed of sound in the room, $V$ is the volume of the room, $S$ is the surface area, and $a$ is the average of the Sabine Absorption coefficients of all the objects in the room.

The Sabine absorption coefficient is a ratio of how much sound is absorbed or reflected off the surface of an object. This ratio changes based on the frequency of the sound. Rooms tend have more reverb at lower frequencies.

Empirically, the reverberation time of a room can be measured by recording the response of the room to a unit impulse or pink/white noise and seeing how long it takes for the sound to decay by 60 decibels. The measured reverberation times of the OEDK classroom, an acoustically desirable room, and a heavily echoic room are displayed below.

Reverberation time is a good way to diagnose how badly a room echoes a generated signal. The actual echo cancellation process involves digitally filtering out the decaying copies of the generated speech signals that cause the room’s poor reverberation times.