b) If the displacement, y, for the string described in part a), can be modelled, at any position z between z = 0 and at

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B If The Displacement Y For The String Described In Part A Can Be Modelled At Any Position Z Between Z 0 And At 1 (43.63 KiB) Viewed 40 times

B If The Displacement Y For The String Described In Part A Can Be Modelled At Any Position Z Between Z 0 And At 2 (63.83 KiB) Viewed 40 times

B If The Displacement Y For The String Described In Part A Can Be Modelled At Any Position Z Between Z 0 And At 3 (63.83 KiB) Viewed 40 times

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 = Z, and at any time, t, by: y(z, t) = sin(wt + kz) - sin(wt - kz) mm = i) Find the displacement at z = 0.42m if t = 0.9 x 10-s. (4 marks) ii) Find the velocity of the string at z = 0.35m and t = 2ms. (6 marks)

Q4. a) The fundamental frequency, f (Hz), of a string of length 2 (m), attached at either end, so that the tension is T (N), is given by: f 21 where p is mass per unit length of the string (kg/m), ) Find the following partial derivatives: af af af and а от др (6 marks) ii) Calculate f based on the following values: L = 1.05m, 7 = 44.1N and p = 0.25 x 10kg/m (1 mark) 11) 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. 7 and p are only accurate to +1% (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 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.