Reverberation time is the most fundamental concept for the evaluation of an indoor acoustical field and is a parameter expressing the length of the sound. Reverberation time is the time, expressed in a second unit, for which reverberation energy density becomes first one million (-60 dB) in comparison with energy density just before stop of the sound source, when the sound is stopped abruptly after the sound radiated in the room reaches an equilibrium. Theory of reverberation is introduced in assumption of diffusible sound field in the room and hence effect thereof does not change even if the sound absorbing material is placed in any position. In any position of the sound source and observation, reverberation time does not change [1.]. Measuring method for reverberation time will be described in the following sections.

Here is a measuring method for reverberation time of an architectural sound [2,] and reverberation measurement by square integral calculus [3,] [4,] [5,] and [6] as sound measurement technique by applying digital signal processing.

Measuring method for reverberation time of architectural sound Fig. 1 expresses general measuring method for reverberation time. A normal band noise is used for the sound source. The band noise is intermittently radiated from the speaker placed in 1 point of the room at a time interval of some seconds. The sound is received by using the non-directional microphone in a measuring point selected so as to distribute as evenly as possible in the room.

Fig. 1. Block diagram of measurement of reverberation time

Analysis was carried out for each octave or 1/ 3 octave band. Attenuation of reverberation time is measured in several times after stop of the sound source in respective measuring points to calculate an average thereof. Attenuation of reverberation is normally recorded by linearizing attenuation of a sound pressure (practical value) by using a high speed level recorder. By reading slope thereof by using a protractor for exclusive use, reverberation time is yielded. In the room of high diffusibility, linear attenuation is observed. However, in occasion, bending may be found in a curve observed. This is a phenomenon often occurring in a room of low diffusibility and caused by leaving of a low order mode of delayed attenuation following attenuation of three-dimensional mode of a large energy.
A frequency used for measuring reverberation time is 63 Hz to 8 Hz in the octave band in an auditorium in which acoustic characteristics are particularly important. However, 125 Hz to 4 Hz in the octave band is occasionally used for easy measurement. After measurement, the resulting values in many measuring points are averaged for each band to yield reverberation time of the room.

General acoustic measurement has a standing signal as the object. In such case, an effective value (RMS value) of a measuring signal such as the sound pressure is measured. On the other hand, in the case where a non-standing signal is the object, square time integral value of the signal is often measured. Fig. 2 expresses a simplified measuring system in which the sound is radiated from 1 point and received in another 1 point in measurement of indoor acoustical characteristics.

Fig. 2 Relation between input and output of a linear system

After random noise n(t) is inputted in a linear system and divided by time (t = 0,) the following equation is held between the output yd(t) and the impulse response h(t) of the system (according to M. R. Schroeder.)

(1)

In collection of the present data, measurement was carried out mainly for impulse response of the room, impulse response in each room can be used, and onetime measurement allows calculating reverberation time and therefore reverberation time was calculated by using square integration. Reverberation curve can be yielded by using an attached [sample program]. In this reverberation curve, reverberation time is the time in which attenuation becomes 60 dB. However, in practice, square integration value does not frequently attenuate to 60 dB. As an example, Fig. 3 shows the reverberation attenuation curve yielded from impulse response measured. As described above, in the case where attenuation does not reach 60 dB, reverberation time is generally calculated from the slope of the attenuation curve. In other words, in the interval in which the slope of the attenuation curve is prominent, a delta (gradient) in the interval is calculated and the time when it is attenuated up to 60 dB is estimated. In Fig. 3, on the basis that attenuation between two points selected is 20 dB, reverberation time is three times (60 dB/ 20 dB) the time in this interval.

Fig. 3. Example of measurement of reverberation attenuation based on impulse response measured according to impulse square integration.

1. Download [sample program].
2. Unpack rcurve.dat file.
3. Execute make -f Makefile.
4. rcurve -1 infile -o outfile (Where, infile and outfile are float (4 bytes))
5. Plot the outfile on a graph to yield the reverberation curve.

[1] The Acoustical Society of Japan, "The Dictionary of Acoustical words," CORONA PUBLISHING CO., LTD., pp. 217, 1988, (in Japanese).

[2] Minoru Nagata, ''Architectural Acoustics,'' CORONA PUBLISHING CO., LTD., pp. 126-127, 1988, (in Japanese).

[3] M. R. Schroeder, 'New method of measuring  reverberation time'', J. Acoust. Soc. Am, Vol. 37, pp. 409, 1965.

[4] Hiroo Yano, and Hideki Tachibana, "Acoustical Measurements by Square-Integration Method," Acoustical Technology, Vol. 6, No. 3, pp. 241-245, 1977, (in Japanese).

[5] Minoru Nagata, ''Architectural Acoustics,'' CORONA PUBLISHING CO., LTD., pp. 136-137, 1988, (in Japanese).

[6] Juro Ooga, Yoshio Yamazaki, and Yutaka Kaneda, "Acoustic System and Digital Processing for Them," CORONA PUBLISHING CO., LTD., pp. 163-164, 1995, (in Japanese).