A tuning fork of frequency 542 Hz is placed near the top of the pipe shown in the Figure. The water level is lowered so that the length L slowly increases from an initial value of 20.0 cm. Determine the next two values of L that correspond to resonant modes. (Assume that the speed of sound in air is 343 m/s.)

The wavelength times the frequency is the velocity of sound, so lambda = c / f At a frequency of 542 Hz and speed 343 m/s the wavelength is 0.633 m (63.3cm)

If the tube is open at the top there is a maximum at the top and a node at the bottom at resonance. i.e. at L = lambda / 4 The next resonance occurs at 3 lambda/4 then 5 lambda/4 etc.

these correspond to 63.3 / 4 = 15.825 cm.................shortest