b) [5 marks] Given a one-dimensional (1-D) string of length L with its both ends held fixed, i.e. u(0,t) = 0 = u(L,t). The method of separation of variables is used to solve for the 1-D wave vibration or propagation on this string. The solution can be expressed as 00 711 . Mat, t) = 2 cu sin (73?) cos (I): ) , o Is wave speed 11:] Which of the following initial displacement distributions, i.e. u(a:,0) = f(a:), would result in having the coefficients en's decreased fastest with the integer index n? There is no initial velocity, i.e. %(m, 0) = 0. Justify your answer. (i) (ii) (iii) fix) f (1") f (3:) [Answer]