Equation to calculate critical number of guests that make a party too noisy.

by David Ng



N0 = the critical number of guests above which each speaker will try overcome the background noise by raising his voice
K = the average number of guests in each conversational group
a = the average sound absorption coefficient of the room
V = the room’s volume
h = a properly weighted mean free path of a ray of sound
d0 = the conventional minimum distance between speakers
Sm = the minimum signal-to-noise ratio for the listeners

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As derived by William R. MacLean, “On the Acoustics of Cocktail Parties,” Journal of the Acoustical Society of America, January 1959, 79-80 (link | pdf). Text via Futility Closet.