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Matakuliah Tahun : K0124 / Matematika Teknik II : 2006/2007 PERTEMUAN 14 VIBRATING STRING EQUATION 1 2 2 y 2 y a 2 t x 2 This equation is applicable to the small transverse vibrations of a taut, flexible string, such as violin string, initially located on the x axis and set into motion. 2 The function y(x, t) is the displacement of any point x of the string at time t. The constant a2 = T / , where T is the (constant) tension in the string and is the (constant) mass per unit length of the string. 3 It is assumed that no external forces act on the string but that it vibrates only due to its elasticity. 4 The equation can easily be generalized to higher dimensions as for example the vibrations of a membrane or drum head in two dimensions. 5 In two dimensions, for example, the equations is 2 2 2z z z 2 a 2 2 2 t y . x y Y =(x, t) 6 TERIMA KASIH 7