The content of this page was originally posted on August 30, 2005 (updated January 16, 2024).

Reverberation Time in a Small (but very reverberant) Room

Discovering the Empty Room

The data, plots, recordings, and photographs on this page were collected and created while I was a member of the Physics faculty at Kettering University, Flint MI. Sometime around February/March 2001 I was walking out of the ground floor of the Academic Building to the faculty parking lot to drive home. As I was walking down the hallway, I noticed a normally locked door was open and saw that the open door provided access to an empty room. This room used to serve as the athletic crib connected to the old gymnasium (which was, itself, badly in need of repair and was closed to access while being used as junk storage while waiting for renovation).

My curiosity aroused, I went through the open door discovered that this empty room had some remarkable acoustical properties (including a surprisingly long reverberation time). So, I immediately ran back upstairs to my lab, called my wife to tell her I would be late for supper, and grabbed some equipment to make some recordings of the reverberation time -- expecting that this would be my one chance to have access to this temporarily vacant (and normally locked) acoustic space.

A few weeks later, I noticed that the door happened to be open once again as I was leaving and this time I noticed that carpet had been laid in the room. So, once again I called my wife to say I'd be late for dinner again, brought down the recording equipment and made some new recordings with carpet on the floor. The carpet noticeably reduced the reverberation time. Unfortunately I was not able to gain access (even after asking) to this space once the renovations had been completed and desk carrels and furniture had been installed.

Measured Room Response

The room dimensions were: 9.25 m long, 7.65 m wide, and 3.15 m high. The walls were painted cement blocks, and the floor was unpainted concrete (later covered with carpet). The ceiling was not flat nor smooth, but has a number of cement "cross beams" resulting in lots of small nooks and crannies which would increase the reverberation time by providing numerous reflective surfaces for sound to bounce around. I used a Tascam DA-P1 portable DAT recorder and an Audio Technica AT4041 microphone to make recordings of the room response to a hand clap and to human speech.

Hand Clap (room empty) (0.359 MB wav file)
Hand Clap (with carpet) (0.455 MB wav file)
Speech (room empty) (0.467 MB wav file)
Speech (with carpet) (0.560 MB wav file)

Estimated Reverberation Time

The Sabine equation for estimating the reverberation time, $T_{60}$ is $$ T_{60} = \frac{55.25 V}{c\,S\,\bar{\alpha}} $$ where $V$ is the volume of the room in cubic meters, $c = 343 {\rm m/s} $ is the speed of sound in air, $S$ is the total surface area of the room in square meters and $\bar{\alpha}$ is the average absorption coefficient for the room, calculated from $$ \bar{\alpha} = \frac{\alpha_1 S_1 + \alpha_2 S_2 + \dots + \alpha_n S_n}{S} $$ where $\alpha_n$ are the individual absorption coefficients for each surface $S_n$ and $S$ is the total surface area of the whole room.

The absorption coefficients $\alpha$ for cement block walls and floor are:

Frequency (Hz)	125	250	500	1000	2000	4000
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 calculated 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

The composite photos below show what the room looked like on my two visits. I apologize for the lack of photo quality - these photos were taken in 2001 (long before iPhones existed) using an early digital camera with limited zoom and no panoramic ability and the individual photographs, with different lighting, were combined to form the composite images shown.

Composite photographs of the room with carpet on the floor

photograph of an empty room with carpet on the floor

Measured Reverberation Time

I used a SRS 785 FFT analyzer (using Octave Band and waterfall plot options) to process the hand clap audio recordings. The FFT analyzer was set to sample the sound file every 8 ms, for a total of 400 measurements covering 3.2 seconds. The FFT 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 measured time traces for the 500 Hz, 1000 Hz, and 2000 Hz octave bands are shown below (respectively from left-to-right). 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 from the 1000 Hz plot in the middle, I estimate a measured reverberation time of 3.3 seconds for the empty room and 1.6 seconds for the room with carpet. These results are about 0.7 seconds longer than the results from the Sabine equation calculations above. This is most likely due to the fact that the Sabine equation assumes smooth surfaces and does not account for the cavities between the ceiling cross-beams which trap sound and allow it to bounce around before returning it to the rest of the room, thus lengthening the reverberation time.

It is also true that the Sabine equation assumes a relatively uniform distribution of absorption, which is not true for our carpeted room since the carpet is only applied to one of the six room surfaces. There are other equations available which might provide better estimates of the reverberation time for this room.