Let length be $l$ .
$f=\sqrt{\frac{T}{\mu}} \times \frac{1}{2 l} \quad \dots (i)$
$f=\sqrt{\frac{T}{\mu}} \times \frac{4}{2 l} \quad \dots (ii)$
or $f=\sqrt{\frac{T}{\mu}} \times \frac{4}{6 l} \quad \dots (iii)$.
Equating $(i)$ $(ii)$ and $(i)$ and $(iii)$
$\sqrt{\frac{T}{T_1}}=4$ and $\sqrt{\frac{T}{T_2}}=\frac{4}{3}$
Put $T=32 \,N$
$\frac{32}{16}=T_1 \frac{9}{16} \times 32=T_2$
$T_1=2 N T_2=18 \,N$
of the options on $T_1$ is right.
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$(a)$ $\left(x^2-v t\right)^2$
$(b)$ $\log \left[\frac{(x+v t)}{x_0}\right]$
$(c)$ $e^{\left\{-\frac{(x+v t)}{x_0}\right\}^2}$
$(d)$ $\frac{1}{x+v t}$
