External Surface-Absorption Cross Section of a Pipe Organ

Abstract

The total sound absorption due to a rank of organ pipes arises chiefly from internal resonance losses and also from energy dissipation taking place at the external surfaces of the pipes. The first contribution has been discussed elsewhere [A. H. Benade, J. Acoust. Soc. Am. 38, 780–789 (1965)], and the second is reported here. Scattering of a plane wave incident obliquely on a long circular cylinder is calculated, and the results are used to find the energy absorbed via viscosity and also via the short-circuiting of the wave's temperature fluctuations produced by an isothermal boundary. It is shown that an absorption coefficient can be defined for the pipe surface that is approximately independent of the radius/wavelength ratio. The corresponding coefficient for viscous and thermal losses at a plane surface is also calculated. The result are ᾱcyl = 2.3⋅10−5(ω)12 and ᾱPLANE = 6.8⋅10−5(ω)12. The latter result agrees with a calculation by Walther [J. Acoust. Soc. Am. 33, 127–136 (1961)]. Computation of the absorption by a rank of pipes is simplified by using the scaling principles followed by organ builders. It is shown that the external absorption is negligible below 500 Hz, and is only about 0.06 m2 at 2000 Hz for a 73-pipe rank centered at middle C.