(a) In a resonance column experiment, a tuning fork of frequency `400 Hz` is used. The first resonant is observed when the air column has a length of `20.0 cm` and the second resonance is observed when the air column has a length of `62.0 cm`. (i) Find the speed of sound in air. (ii) How much distance above the open end does the pressure mode form?
(b) A piston is fitted in a cylindrical tube of small crosssection with the other end of the tube open. The tube resonates with a tuning fork of frequency `512 Hz`. The piston is gradually pulled out of the tube and it is found that a second resonance occurs when the piston is pulled out through a distance of `32.0 cm`. Calculate the speed of sound in the air of the tube.