Distribution of Eigentones in a Rectangular Chamber at Low Frequency Range

According to previous calculations the number of eigentones in a rectangular chamber of volume V with frequencies less than ν is given by N = (4π/3)(Vν3/c3) where c is the velocity of waves. This relation only holds [or very large numbers of eigentones, i.e., when ν is very high. For lower frequency ranges the corrected value of N has been found to be N = 4π3 Vν3c3 + π4 Sν2c2 + 12 Lνc, where S is the total surface area and L the sum of three dimensions of the chamber. This formula is suggested to be used in acoustic problems with V taken as the volume, S the total surface area and L the sum of half the perimeter and the height of the chamber.