Use the worked example above to help you solve this problem. Figure a shows a simple apparatus for demonstrating resonance in a tube. A long tube open at both ends is partially submerged in a beaker of water, and a vibrating tuning fork of unknown frequency is placed near the top of the tube. The length of the air column, L, is adjusted by moving the tube vertically. The sound waves generated by the fork are reinforced when the length of the air column corresponds to one of the resonant frequencies of the tube. Suppose the smallest value of L for which a peak occurs in the sound intensity is 8.81 cm. Take the speed of sound to be 338 m/s.
a) With this measurement, determine the frequency of the tuning fork.
b) Find the wavelength and the next two air-column lengths giving resonance.