Q4. a) The fundamental frequency, f (Hz), of a string of length L (m), attached at either end, so that the tension is T

[answerhappygod]

Q4 A The Fundamental Frequency F Hz Of A String Of Length L M Attached At Either End So That The Tension Is T 1 (37.15 KiB) Viewed 19 times

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: 1 T f 2L m and where p is mass per unit length of the string (kg/m). i) Find the following partial derivatives: af af af al' at др (6 marks) ii) Calculate f based on the following values: L = 1.05m, T = 44.1N and p = 0.25 x 10-kg/m (1 mark) iii) 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, 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 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. (6 marks)