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Q4. a) The fundamental frequency. f (Hz), of a string of length L (m). attached at either end, so that the tension is T (N), is given by f 2L where 1) il) p is mass per unit length of the string (kg/m). Find the following partial derivatives af of of alat and др (6 marks) Calculate f based on the following values L = 1.05m, T = 44.1N and p = 0.25 x 10-kg/m (1 mark) Derive an equation to estimate the maximum error for fin Hz, and use it to find this error under the assumption that the values given above for L. T and p are only accurate to +1% II) (8 marks) b) If the displacement, y, for the string described in part a), can be modelled, at any position z between z = 0 and at z = L, and at any time, t. by y(z. t) = sin(wt+kz) - sin(wt - kz) mm 1) Find the displacement at := 0.42m ift = 0.9 x 10's (4 marks) ii) Find the velocity of the string at z = 0.35m and t = 2ms. (6 marks)