Browsing by Author "Ngonibi, Matthew Kpabu Ngala"

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    Boundary – Value Problems with Particular Reference to the African Rectangular Drum
    (2011-06-20) Ngonibi, Matthew Kpabu Ngala
    Drums are part of most Africa cultures, and produce different sounds according to their shapes and sizes. The purpose of this study is to explain the mathematics involved in the vibration of a rectangular drum. Hence a rectangular drum was modeled for that purpose. The wave equation in the rectangular Cartesian coordinates was solved with boundary conditions dictated by the fact that the edges of the drum were fixed. The initial condition was that, the velocity was zero for the entire membrane. The double Fourier coefficients were computed and truncated and presented as 3 x 3 matrices. The computed Fourier coefficients enabled the identification of the normal modes. This was done for four cases of solutions for certain polynomials in x and y. The regular symmetry of the drum appears to influence the symmetry of the solutions. The study found that, the sound waves produced from all the four cases, moved crest and trough with cases one, two and four recording nodal points and case three having none.