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Wallace Sabine was an assistant professor of physics at Harvard in 1898.At that time, a lecture hall at the university called Fogg Hall had such a bad echo that it couldn’t be used for lecture classes.

Sabine was asked to determine what factors were controlling the length of time it took for the sound to die away in the hall and that were contributing to the echo effect. He decided to use a 512 Hz note as a reference point, and then he timed how long it took the sound to die away completely.

After making thousands of measurements in various buildings at Harvard, he discovered something that he called "reverberation time."This phenomena was related to the volume of the room and the absorbency of the materials on the room’s surfaces.

Sabine started making his calculations about this with several assumptions. He assumed that the sound field in a room was perfectly diffuse; absorption was evenly distributed throughout the room; and that the reverberation time obtained for a 512 Hz tone would be representative of all frequencies in the room.

He used his assumptions to come up with an equation for calculating the reverberation time of a room, and he published his findings in October 1898.

Sabine’s equation stated that:

The reverberation time (RT) in seconds is proportional to the ratio of the room volume V (in cubic meters) and the total absorption A of all the surfaces in the room. The constant of proportionality is based on the speed of sound, but for the purposes of rooms at normal atmospheric pressure and temperature (20°C), 0.161 is an acceptable value.

Thank you for your answer. Unfortunately it doesn't address the key point of my question. How did he arrive at 0.161 as the constant value? Where did that figure come from? Is it a coincidence that 0.161 is a sixth?