Theory of the Indian musical drums-Part I

Abstract

The paper contains a discussion of the normal modes of vibration of a symmetrically loaded membrane in which the surface density varies as an inverse fractional power of the radial distance from the centre, with a view to ascertain how far a law of density of this type enables the harmonic sequence of tones observed in the Indian musical drum to be approximated to. It is shown that for a law of density varying in inverse proportion to the radius, the first four modes with nodal diameters only, form an approximate harmonic sequence with the fundamental. With this law of loading, however, the relative frequencies of the symmetrical modes remain entirely unaffected (though their interior nodal circles contract), while the frequencies of the modes having both nodal diameters and nodal circles, require a greater degree of loading than that stated above to fall into the same harmonic sequence. The results thus show clearly that a type of loading so highly concentrated at the centre cannot succeed in reproducing completely the observed results. The indications are that a more widely distributed load such as is actually employed should theoretically be necessary to achieve the desired purpose.