The speed of transverse wave in aluminium wire is 1 10 times the speed of longitudinal wave in the wire. The stress in the wire is (Young's Modulus of Al = 10¹⁰ Pa)

Step-by-step solution

The speed of a transverse wave in a stretched wire is given by v_t = T = T A = , where T is the tension, is the linear mass density, A is the cross-sectional area, is the density, and is the stress in the wire. The speed of a longitudinal wave in the wire is given by v_l = Y , where Y is the Young's modulus. Given that v_t = 1 10 v_l , substituting the expressions yields: = 1 10 Y Squaring both sides gives: = 1 100 Y = Y 100 Substituting Y = 10¹⁰ Pa: = 10¹⁰ 100 = 10^8 Pa. Answer: 10^8 Pa