Wave Deflections of Some Ghanaian Musical Instruments; The Case of Fontomfrom and Atumpan
Godfried O. Lartey, Gabriel Obed Fosu, Divine M. Adofoli · International Journal of Applied Mathematics & Statistics/International journal of applied mathematics and statistics · 2019
This paper explores the mathematical vibrations of the Fontomfrom and Atumpan drums using the two-dimensional wave equation. This wave equation is transformed into a Fourier-Bessel function to determine the wave profiles of these drums. Simulations analysis is performed to obtain the deflections of these drums at different radii and time based on the quadratic and the cubic radial function. The quadratic function gives evidence of slight harmonic vibrations after the rhythmic vibration at the beginning of the initial deflection at the center. This gradually dies off close to the edge of the drums. In contrast, the vibrations of the cubic function as well die off at the edge of these drumheads but have greater membrane vibrations in the neighborhood of the center.