Modes of vibration of the Indian drum dugga or left-hand thabala

Abstract

The dugga or the left-hand thabala is a companion drum to the right-hand thabala and the two together are widely used in India. The vibration characteristics of the latter which has a symmetrically loaded membrane were discussed previously where it was shown how this drum produces harmonic overtones. The left-hand thabala also has a loaded drumhead, but the loading is here eccentric. The boundary value problem of this drumhead is not separable, and hence there is no readily available method for computing its characteristic frequencies. An approximate theory for computing the frequencies of the lower modes is here developed under the assumption that for these modes the effect of the (unloaded) annular region on the loaded region may be replaced by a suitably determined elastic support around its boundary. This leads to the boundary value problem of a membrane with an elastic boundary support whose stiffness constant per unit length is a function of the polar angle. The problem is still unseparable, but the eigenvalues can be now computed by a boundary perturbation technique from those of a membrane with a boundary support of constant stiffness. Computed and measured frequency ratios agree within seven percent or better.