Reverberation Time

• Reverberation time (RT60 or $T_{60}$) is defined as the time it takes for the sound in a room to decrease by 60 dB from its original level, after the sound source is stopped. It generally varies with frequency.

• In a bare room, where all surfaces absorb the same fraction of the sound that reaches them, the theoretical reverberation time is proportional to the ratio of volume to surface area.

• In the late 1890s, Wallace Sabine proposed an empirical formula to calculate reverberation time from the dimensions (in meters) of a room as:
    $$RT60 = 0.161 V/A,$$ (1)
  where $V$ is the volume of the room in cubic meters and $A$ is the effective “total absorption area.”

• The “total absorption” area is calculated as the sum of all surface areas in the room, each multiplied by its respective absorption coefficient for a particular frequency.

• A low absorption coefficient indicates a more reflective material.

• Typical frequencies for which absorption coefficients are determined are 125, 250, 500, 1000, 2000, and 4000 Hz.

• Air contributes a substantial amount to the absorption of high frequency sound and can be accounted for (in a simplistic way) in the formula for reverberation time as RT60 = 0.161 $V/(A + mV)$, where $m$ is a constant that varies with air temperature, humidity, and frequency.

• More accurate estimations for $RT60$ are nowadays found from modeled or measured room impulse responses.

• The optimum reverberation time of a room is dependent on the use for which it is designed (speaking, chamber music, opera, orchestral music, organ, etc.). RT60 values for some spaces are:
  • Musikverin, Vienna: 2.0 sec.
  • Carnegie Hall, New York: 1.8 sec.
  • Disney Hall, Los Angeles: 1.85 sec.
  • Hagia Sophia, Istanbul: $\approx 6.0$ sec.
  • Churches: 2.0 – 5.0 sec.
  • Classrooms: 0.5 – 1.0 sec.

• Modern technologies, such as the Meyer Sound's Constellation system, can extend the apparent reverberation time of a room. If one wishes to lower the $RT60$ of a room, curtains or other acoustic absorbers can be introduced.