Dah-You Maa and the many facets of modal density

Abstract

Maa’s formula for the modal density of a room is known to everyone in acoustics. The wonderful part of it is that it so logical and direct that you don’t have to memorize or look it up - you can simply re-derive it on the spot. When it was published by Maa in 1939, there was a competing formulation by Dick Bolt that had the same volume dependent term, but was quite different in the surface area and edge length terms. But by the time of the landmark paper by Morse and Bolt in 1944 [“Sound waves in rooms”, Rev. Mod. Phys. 16(1) (1944)], Maa’s formula had won and was the relationship cited by Morse and Bolt. The uses of modal density in the response statistics of acoustical spaces and structures for the purposes of estimating impedances, energy flow, and phase statistics have grown as recognition of this fundamental property of resonant systems has grown.