Sound hole sum rule and the dipole moment of the violin

It is shown both theoretically and experimentally that at long enough wavelengths the radiation pattern of a violin, or of any similar instrument with a sound hole in its shell, becomes that of a dipole. The transition from this region to the one in which the monopole dominates is traced in detail. The experimental method used to measure the ‘‘radiativities’’ of the violin, that is, the amplitudes of the various multipole moments developed per unit force applied to the bridge by the vibrating string, utilizes an extension of the reciprocity principle in which the multipole fields play the rôle of generalized coordinates. Absolute measurements of the radiativity are obtained, and their phases and amplitudes explained in terms of the mechanical motions of the violin shell and the enclosed air.