Answer
We can rank the standing waves in order of frequency, from largest to smallest:
$e \gt b \gt c \gt a = d$
Work Step by Step
We can write an expression for the frequency in each case:
(a) $f_1 = \frac{v}{\lambda_1} = \frac{v}{4L}$
(b) $f_3 = \frac{v}{\lambda_3} = \frac{v}{4L/3} = \frac{3v}{4L}$
(c) $f_1 = \frac{v}{\lambda_1} = \frac{v}{2L} = \frac{2v}{4L}$
(d) $f_1 = \frac{v}{\lambda_1} = \frac{v}{4L}$
(e) $f_2 = \frac{v}{\lambda_2} = \frac{v}{L} = \frac{4v}{4L}$
We can rank the standing waves in order of frequency, from largest to smallest:
$e \gt b \gt c \gt a = d$
