Transverse waves of same frequency are generated

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

a) 1:3/2 b) √2:1
c) 1:2 d) 1:2√2

v = root of (T/m)
where T is tension and m is mass per unit length
So, m = M/L = Vol*density/L
So, m = A*L*density/L
So, m = A*density = pi*(r^2)*density
So, v = root of (T/(pi*(r^2)*density))
So, v is proportional to (?T)

So, va/vb = (root of (Ta/Tb))*(rb/ra)
So, va/vb = (root of(1/2))*(1/2)
So, va/vb = 1/(2*root 2)