Answer
$f_{max,1}$ must be multiplied by $~~2$
Work Step by Step
We can find the path length difference:
$\Delta L = 19.5~m-18.3~m = 1.2~m$
To produce fully constructive interference, $\frac{\Delta L}{\lambda} = 1, 2, 3,...$
Then: $\lambda = \frac{\Delta L}{1}, \frac{\Delta L}{2},\frac{\Delta L}{3},...$
We can find the lowest frequency that produces fully constructive interference:
$f_{max,1} = \frac{v}{\lambda}$
$f_{max,1} = \frac{v}{\Delta L/1}$
$f_{max,1} = \frac{v}{\Delta L}$
$f_{max,1} = \frac{343~m/s}{1.2~m}$
$f_{max,1} = 286~Hz$
We can find an expression for $f_{max,2}$:
$f_{max,2} = \frac{v}{\lambda}$
$f_{max,2} = \frac{v}{\Delta L/2}$
$f_{max,2} = \frac{2~v}{\Delta L}$
$f_{max,2} = 2\times ~\frac{v}{\Delta L}$
$f_{max,2} = 2\times ~f_{max,1}$
$f_{max,1}$ must be multiplied by $~~2$
