Absorption Cross Section of a Pipe Organ Due to Resonant Vibration of the Pipe Walls

Abstract

The sound absorption by a rank of organ pipes from a sound field arises chiefly from air-column resonance losses plus boundary-layer dissipation at the external surfaces of the pipes. These processes have been discussed elsewhere [A. H. Benade, J. Acoust. Soc. Am. 38, 780–798 (1965) and 41, 32–38 (1967)]. The pipe walls themselves can vibrate when driven by the sound field, so that there is a further absorption of energy. The present report shows (on the basis of measured elastic and damping constants of pipe metal) that the wall-vibration resonance-absorption cross section for a complete rank of cylindrical organ pipes is negligible, being less than 1 cm2 at 62 Hz, falling to less than 0.05 cm2 at 2000 Hz. For elliptical pipes, the absorption can be a hundred fold larger, but it is still negligible as compared with the other absorption processes. It is also shown that the reradiation due to wall vibrations is so small as to justify the assumption, on which an earlier calculation of external surface absorption was based, that the pipes scatter as though they are essentially rigid.