Tiwari Sankalp, Gupta Anurag
Department of Mechanical Engineering, Indian Institute of Technology, Kanpur 208016, India.
J Acoust Soc Am. 2017 Apr;141(4):2611. doi: 10.1121/1.4979782.
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.
通过将印度乐器塔布拉鼓理想化地视为一个由刚性圆柱形腔体支撑的复合膜，研究了空气负载对其声学特性的影响。假设声辐射是唯一的耗散源，使用格林函数方法求解了膜振动和声压的耦合边值问题。结果表明，空气负载仅有助于微调右手塔布拉鼓中复合膜的谐波，但显著改善了左手塔布拉鼓中的谐波。在这两种情况下，它都增加了音乐上重要模式的衰减时间。以适当定义的误差作为目标函数，找到了最佳的塔布拉鼓设计，其产生了最和谐的频谱。发现所获得的结果与塔布拉鼓的实际设计一致。还尝试了打击乐器的模态声音合成。
