Transverse waves of the same frequency are generated in two steel wires A and B . The diameter of A is twice that of B and the tension in A is half that in B . The ratio of the velocities of the waves in A and B is

Step-by-step solution

The velocity of transverse waves is given by v= T m where, T= Tension and m= mass per unit length of the wire. If r is the radius of the wire and its density then, m= r^2 v= T m = T r^2 v_A= T_A r_A and v_B= T_B r_B Now, v_A v_B = T_A T_B r_B r_A r_A=2 r_B and T_A= 1 2 T_B Hence, v_A v_B = 1 2 2