Two wires A and B of the same material are stretched between the same pair of rigid supports, but they differ in length and linear mass density. For wire A, LA=80cm and μA=0.012kgm−1. For wire B, LB=50cm and μB=0.020kgm−1. Each wire is kept under a (possibly different) tension and both are observed to have the same fundamental frequency.
(i) Derive an expression connecting the tensions TA and TB in terms of the given lengths and mass densities, based on the condition of equal fundamental frequencies.
(ii) Using the given numerical values, calculate the ratio TA:TB.
(iii) If the tension in wire A is 120N, determine the numerical value of TB.