Answer
The ratio of A's frequency to B's frequency is $\frac{3}{4}$
Work Step by Step
In A's column, the next-to-lowest resonant frequency has a wavelength of $\lambda_3 = \frac{4L}{3}$. We can find an expression for the frequency of tuning fork $A$:
$f_A = \frac{v}{4L/3} = \frac{3v}{4L}$
In B's column, the next-to-lowest resonant frequency has a wavelength of $\lambda_2 = \frac{2L}{2} = L$. We can find an expression for the frequency of tuning fork $B$:
$f_B = \frac{v}{L}$
We can find the ratio of A's frequency to B's frequency:
$\frac{f_A}{f_B} = \frac{3v/4L}{v/L} = \frac{3}{4}$
The ratio of A's frequency to B's frequency is $\frac{3}{4}$
