Answer
We can rank the strings according to the fundamental frequencies, from largest to smallest:
$d \gt a \gt b = c \gt e$
Work Step by Step
We can write an expression for the wave speed along a string:
$v = \sqrt{\frac{F}{m/L}} = \sqrt{\frac{F~L}{m}}$
We can find an expression for the fundamental frequency:
$f = \frac{v}{\lambda}$
$f = \frac{\sqrt{\frac{F~L}{m}}}{2L}$
$f = \frac{1}{2}~\sqrt{\frac{F}{m~L}}$
We can find an expression for the frequency in each case:
(a) $f = \frac{1}{2}~\sqrt{\frac{F}{m~L}}$
(b) $f = \frac{1}{2}~\sqrt{\frac{F}{m~(2L)}} = \frac{\sqrt{2}}{2}\times \frac{1}{2}~\sqrt{\frac{F}{m~L}}$
(c) $f = \frac{1}{2}~\sqrt{\frac{F}{(2m)~L}} = \frac{\sqrt{2}}{2}\times \frac{1}{2}~\sqrt{\frac{F}{m~L}}$
(d) $f = \frac{1}{2}~\sqrt{\frac{2F}{m~L}} = \sqrt{2}\times \frac{1}{2}~\sqrt{\frac{F}{m~L}}$
(e) $f = \frac{1}{2}~\sqrt{\frac{F}{(2m)~(2L)}} = \frac{1}{2}\times \frac{1}{2}~\sqrt{\frac{F}{m~L}}$
We can rank the strings according to the fundamental frequencies, from largest to smallest:
$d \gt a \gt b = c \gt e$
