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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 p is mass per unit length of the string (kg/m), i) and ii) Find the following partial derivatives: af af af al' at др (6 marks) Calculate f based on the following values: L = 1.05m, T = 44.1N and p = 0.25 x 10-3kg/m (1 mark) Derive an equation to estimate the maximum error for f in 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%. iii) (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 = i) Find the displacement at z = 0.42m ift = 0.9 x 10-3s. (4 marks) ii) Find the velocity of the string at z = 0.35m and t = 2ms.