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Appendix 4: Deriving the Reverberation Time Equation

Clearly the length of time that it takes for sound to die is a function not only of the absorption of the surfaces in a room but also a function of the length of time between interactions with the surfaces of the room. We can use these facts to derive an equation for the reverberation time in a room. The first thing to determine is the average length of time that a sound wave will travel between interactions with the surfaces of the room. This can be found from the mean free path of the room which is a measure of the average distances between surfaces, assuming all possible angles of incidence and position. For an approximately rectangular box the mean free path is given by the following equation: ...

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