Two cylindrical vases 1 and 2, are open at the top and have
equal cross sections, but vase 2 is taller than vase 1, as
shown. Both vases are filled to equal heights with water.
The frequencies of the fundamental standing waves in the
air columns are F1 and F2, respectively. Which of these is
greater?

The frequency of the fundamental standing wave in a closed cylindrical air column (like a vase filled with water) depends on the speed of sound in the air column and the length of the air column.

Given that both vases have equal cross-sections but vase 2 is taller than vase 1, we can assume that the fundamental frequency in vase 2 (F2) will be lower than the fundamental frequency in vase 1 (F1).

This is because the longer the air column (taller vase), the longer the wavelength of the fundamental standing wave, and thus, the lower the frequency.

So, F1 would be greater than F2.