Answer
$\frac{1}{4}T_0$
Work Step by Step
Since we need the two frequencies to be equal $f_1=f_2$, and since the frequency of a standing wave in a string $f_m$ is given by
$$f_m=\dfrac{mv}{2L}=\dfrac{m}{2L}\sqrt{\dfrac{T_s}{\mu}}$$
Thus,
$$\dfrac{1}{ \color{red}{\bf\not} 2 \color{red}{\bf\not} L}\sqrt{\dfrac{T_0}{ \color{red}{\bf\not} \mu}}=\dfrac{2}{ \color{red}{\bf\not} 2 \color{red}{\bf\not} L}\sqrt{\dfrac{T_s}{ \color{red}{\bf\not} \mu}}$$
squaring both sides;
$$T_0=4T_s$$
Therefore,
$$\boxed{T_s=\frac{1}{4}T_0}$$
