Raman first observed that the overtones of the Indian musical drums, Mridanga and Thabala, form a sequence of five natural harmonics, and that they result from nine modes of vibration, some of which are (approximately) degenerate. After a brief review of the previous work on the subject, a theory of these drums is developed in the present paper on the basis that the drumheads of these instruments can be regarded as circularly symmetric membranes with a radial step discontinuity the density. The eigenvalues and eigenfunctions of such a composite membrane are obtained, and it is then shown from a numerical calculation that for suitable ratios between the densities and radii of the two parts, the frequencies and the modes of vibration are in accordance with Raman's observations. Measured values of the frequencies of the first nine modes confirm the approximate degeneracies and the harmonicity indicated by the theory and establish the adequacy of the composite membrane as a mathematical idealization of these drumheads.

The forced vibrations of stretched strings near their resonance frequencies exhibit several features that cannot be explained on the basis of the classical theory. As the driving frequency approaches resonance frequency, the increase in the amplitude of vibration of the string causes a change in its tension and the restoring force becomes nonlinear. Experiment shows that the amplitude response exhibits a downward jump while the driving frequency is being increased and an upward jump at a different frequency while the frequency is being decreased. Moreover, when the amplitude of vibration in the plane of the driving force reaches a certain critical value, which depends upon the magnitude of the driving force, the string acquires a component of motion in a direction normal to the plane of the string and the force. These phenomena are always observed in a more or less conspicuous manner, depending upon the magnitude of the force. When the restriction to infinitesimally small amplitudes of vibration (which is untenable near resonance) is removed, the motion of the string is governed by a pair of nonlinear, partial differential equations. Appropriate solutions of these equations show that the jump phenomena and the nonplanar vibration are the normal pattern of resonance behavior of stretched strings, however small the driving force may be. Response patterns and other results deduced from theory agree closely with those obtained from experiment.

In this paper, subjective studies made on nonexponentially decaying sounds are described. The various decay conditions are realized by changing the position of the pickup microphone in a reverberation room with a highly absorbing sample on the floor. It is shown, by means of articulation tests, that intelligibility of speech is more close to a highly absorbing sample than away from it. It is also shown that the perception of decay is mainly due to the initial portion of a nonexponential decay. The significance of these studies is determining the acoustics of halls is explained. Subiect Classification: 55.20; 70.35; 55.30.

Introduction. Although several problems of heat flow in composite cylinders have been studied, all the cases considered treat the heat flow in the radial direction only [1,2,3]. The case of combined radial and axial heat flow in composite cylinders presents an interesting boundary value problem which has also considerable significance in the theory of vibrations and propagation of electromagnetic waves [4,5,6]. In this paper, we consider a case of combined radial and axial heat flow in the unsteady state in finite cylinders composed of two coaxial parts of different materials. The temperature distribution in the cylinder at any instant under the assumed boundary and initial conditions has been obtained by the use of the Laplace transformation.The procedure is illustrated by a numerical calculation in a particular case.The Problem. Composite cylinder made of two different materials, the inner cylinder 0 < r < a and the outer cylinder a < r 0 (see Fig. 1).

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.