(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.

Explanation

(a) `f = 400 Hz, l_(1) = 20 cm, l_(2) = 62 cm`
(i) `v = 2f (l_(2) - l_(1)) = 2 xx 400(62 - 20) xx 10^(-2)`
`= 336 m//s`
(ii) `e = (l_(2) - 3l_(1))/(2) = (62 - 3 xx 20)/(2) = 1 cm`
(b) `(3 lambda)/(4) - (lambda)/(4) = 32`
`lambda = 64 cm`
`v = f lambda = 512 xx 64 xx 10^(-2)`
`~= 328 m//s`