Effects of air loading on the acoustics of an Indian musical drum

Abstract

The effects of air loading on the acoustical properties of tabla, an Indian musical drum, are investigated by idealizing it as a composite membrane backed by a rigid cylindrical cavity. The coupled boundary value problem for membrane vibration and acoustic pressure, assuming acoustic radiations to be the only source of dissipation, is solved using a Green's function method. It is shown that air loading helps in only fine tuning of the harmonicity of the composite membrane in the right hand tabla, but significantly improves the harmonicity in the left hand tabla. In both cases, it increases the decay time of the musically important modes. With a suitably defined error as the objective function, optimum tabla designs are found, which yield the most harmonic frequency spectrum. The obtained results are found to be consistent with the actual design of the tabla. Modal sound synthesis of the percussion instrument has also been attempted.

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“…In many musical instruments, the sound is produced with missing fundamental like in Timpani and Kim (Boedts, 2020;Thangprasert, 2015). There are many reasons for missing fundamental in instruments, for example in Timpani air loading generates missing fundamental and in Indian drums like Tabla the striking method by the artist creates missing fundamental (Rossing, 1977;Tiwari & Gupta, 2017). Figure 11 shows the frequency spectrum of the note played on the Indian drum, Tabla, with harmonics and here the lowest peak is not in harmonic relation with other peaks.…”

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“…In the field of acoustics of percussion instruments with an air-membrane coupling, instruments such as the tom-tom drum and snare drum [8] and Indian tabla [9], [10] have been considered. Most research is devoted to the timpani or kettledrum [11], [12].…”