Acoustics and Vibration Animations Daniel A. Russell, Ph.D. Graduate Program in Acoustics The Pennsylvania State University All text and images on this page are ©2004-2011 by Daniel A. Russell and may not used in other web pages or reports without permission.

# Reverberation in a Small Room

In the Winter 2001 term I chanced upon a small room in the basement of Kettering University which was being renovated. The room used to be an athletic crib attached to the old gymnasium and it was being converted into a computer research laboratory for one of the ME faculty and his graduate students. The room had some remarkable acoustics (a surprisingly long reverberation time) so I took the chance to make some measurements as the renovations were being completed. A few weeks later I noticed that carpet had been laid in the room, so I brought down the recording equipment and made some new recordings. The carpet noticeably reduced the reverberation time.

### Measured Room Response

The room is 9.25 m long, 7.65 m wide, and 3.15 m high. The walls are painted cement blocks, and the floor was unpainted concrete (later covered with carpet). The ceiling is not flat, but has a number of cement "cross beams" which may increase the reverberation time by providing lots of reflective surfaces for sound to bounce around. Using a Tascam DA-P1 portable DAT recorder and an Audio Technica AT4041 microphone I made recordings of the room response to a hand clap and to human speech.

### Estimated Reverberation Time

The Sabine equation for estimating the reverberation time, T60 is
where V is the volume of the room, c=343 m/s is the speed of sound in air, S is the total surface area of the room. is the average absorption coefficient for the room, calculated from
where 1 are the individual absorption coefficients for each surface S1 and S is the total surface area of the whole room. The absorption coefficients for cement block walls and floor are:
Frequency (Hz)125250500100020004000
Concrete block, painted 0.10 0.05 0.06 0.07 0.09 0.08
Concrete floor 0.01 0.01 0.015 0.02 0.02 0.02
Carpet on concrete 0.02 0.06 0.04 0.37 0.60 0.65
Carpet on foam rubber 0.08 0.24 0.57 0.69 0.71 0.73

Using these tables and equations, I calculate the reverberation time for the 1000 Hz band to be approximately 2.6 seconds for the empty room and about 0.93 seconds for the room with carpet.

Composite photographs of the empty room

Composite photographs of the room with carpet

### Measured Reverberation Time

I used a SRS 785 FFT analyzer (using Octave Band and waterfall plot options) to process the hand clap sound files. The analyzer was set to sample the sound file every 8 ms, for a total of 400 measurements covering 3.2 seconds. The analyzer saves all 400 measurements in a buffer and then allows the user to look at amplitude versus time plots for each individual octave band. The traces for the 500 Hz, 1000 Hz, and 2000 Hz octave bands are shown below (click on each plot for a larger version). The red curve is for the empty room and the black curve is for the room with carpet on the floor. The effect of the carpet in reducing the reverberation time is immediately obvious.

Using the slopes of the 1000 Hz plot, I get a measured reverberation time of 3.3 seconds for the empty room and 1.6 seconds for the room with carpet. Notice that these are about 0.7 seconds longer than the estimate calculations from above. This is most likely due to the fact that the Sabine equation does not account for the cavities in the ceiling which can trap sound and allow it to bounce around before returning it to the rest of the room. One must also remember that the Sabine equation assumes a relatively uniform distribution of absorption (which is not true for our carpeted room). There are other equations available which might provide better estimates of the reverberation time for this room.

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