Reverberation Time

John W. Dooley, Physics Department
Millersville University

If you'd rather sing in the shower than in a library, the reason is probably the difference in reverberation time. Sound made in a room cannot diminish by dispersion, since the sound never escapes the room. The sound intensity decreases because of absorption, by the air as it travels and by the walls as it reflects. The time it takes sound to die away is called the reverberation time.

In "The Science of Sound" by Thomas Rossing, Richard Moore and Paul Wheeler (2002), the reverberation time is taken to be the time for the sound amplitude to fall to 1/1000 of its initial value. With GoldWave, it's easier to take a shorter time: the time to fall to 1/3 of the original amplitude.

Absorption by air does not vary significantly from room to room, but absorption by the walls does. Absorption by the air is relatively small, so if the room allows sound to travel a long distance before striking a wall, the sound will reverberate for a long time. This means that the reverberation time is proportional to a length that characterizes the average distance between surfaces.

In text books, this characteristic length is often calculated using a ratio: the volume of the room divided by the area of the walls, floor, and ceiling. (In a spherical room, that length would be roughly the diameter of the sphere.) The material used to make the walls, floor, and ceiling typically have a strong effect on the reverberation time.

In the figures you can see the reverberation of an impulsive noise in various rooms. Figure 1 shows sound reverberating in a bathroom. Figure 2 shows sound reverberating in a book room. And Fig. 3 shows sound reverberating in a garage. In each case the impulsive noise was make by hitting wood with a screwdriver handle. Click on a figure to enlarge it.

Each graph shows the sound amplitude plotted versus time. In each graph, the scale of the time axis is different. The scales have been adjusted so that the decay occurs mostly within the frame of the image. The reverberation time is estimated by looking at the time scale (in seconds) on the horizontal axis.

The sound in the bathroom, which is small with hard walls and fixtures, decays in about 50 msec, a relatively long time because of the low absorption at the walls.

The bookroom is larger, but has a sofa, a wall of books, and carpet on the floor. Sound dies rapidly in this room, taking less than 10 msec to fall to 1/3 of the original amplitude.

The garage, the largest room, is messy with hard-surfaced objects. Like the bathroom, the garage has a reverberation time of about 50 msec. The larger size compensates for the many reflections from objects in the garage.

Find an echoey room and measure the reverberation. Do the same in a "dead" room. Don't mind the funny looks as you tote around your laptop, microphone and screwdriver. Enjoy.