The fundamental frequency of the stretched string is 

\(f=\frac1{2l}\sqrt{\frac T\mu}\) [T = Tension and μ = mass per unit length]

Here, 

\(\mu=\frac mL=\frac{V\rho}L=A\rho\)

\(f=\frac1{2l}\sqrt{\frac T{A\rho}}\)

If T is halved and A is doubled,

\(f=\frac1{2l}\sqrt{\frac{T'}{A'\rho}}\)

\(f=\frac1{2l}\sqrt{\frac{T'}{A'\rho}}=\frac1{2l}\sqrt{\frac1{2\times2\times A\times\rho}}=\frac12\left(\frac1{2l}\sqrt{\frac T{A\rho}}\right)=\frac12f\)

Thus, the frequency is reduced to half if its tension is halved and the area of cross section of the string is doubled.