Digital Synthesis of Sound Generated by Tibetan Bowls and Bells

Abstract

The aim of this paper is to present methods of digitally synthesising the sound generated by vibroacoustic systems with distributed parameters. A general algorithm was developed to synthesise the sounds of selected musical instruments with an axisymmetrical shape and impact excitation, i.e., Tibetan bowls and bells. A coupled mechanical-acoustic field described by partial differential equations was discretized by using the Finite Element Method (FEM) implemented in the ANSYS package. The presented synthesis method is original due to the fact that the determination of the system response in the time domain to the pulse (impact) excitation is based on the numerical calculation of the convolution of the forcing function and impulse response of the system. This was calculated as an inverse Fourier transform of the system's spectral transfer function. The synthesiser allows for obtaining a sound signal with the assumed, expected parameters by tuning the resonance frequencies which exist in the spectrum of the generated sound. This is accomplished, basing on the Design of Experiment (DOE) theory, by creating a meta-model which contains information on its response surfaces regarding the influence of the design parameters. The synthesis resulted in a sound pressure signal in selected points in space surrounding the instrument which is consistent with the signal generated by the actual instruments, and the results obtained can improve them.

Quality Assessment of a Manufactured Bell Using a 3D Scanning Process

“…The computational model was developed on the basis of continuous wavelet transform (CWT), Shannon entropy cost function and mother wavelet. Gołaś [ 26 ] presented a mathematical model of sound synthesis based on Laplace transforms and the Galerkin method. The developed method of sound synthesis was used to determine the natural surface vibrations and the propagation of sound in its surroundings.…”