Resonance‐Absorption Cross Section of a Pipe Organ

Each chromatic rank of pipes in gu organ provides a set of resonant absorbers for reverberant sound. The averaged internal absorption of pipes resonating near angular frequency ω is $ρ̄ = (2π2/0.06) (c2/ω3) (Γr/Γ) (Γ − Γr)$⁠. The resonance width Γ is the sum of the widths Γ_r, Γ_w, Γ_m, arising from radiation, wall losses, and viscosity in the mouth region. The velocity of sound is c. Organ pipes (radius a and length L) are scaled so that a∼L^β, so that absorption by a pipe that resonates at ω in its nth mode is expressible via the properties of a pipe whose fundamental is ω, with radius a, radiating area S, and mouth end correction E. Many pipes in rank absorb strongly at any given frequency. The major contribution comes from the largest pipes excited in their higher modes. A 73‐pipe rank centered at middle C can give a total resonance absorption as high as 0.5 m² at 62 cps, down to about 0.028 m² at 2000 cps. Absorption by external pipe surfaces (calculated elsewhere) is negligible, except at the highest frequencies.