An open organ pipe of length 0.85m is sounded together with a tuning fork of frequency 340Hz in a hall maintained initially at 20∘C. The speed of sound in air at 20∘C is 343m s−1 and it increases by approximately 0.6m s−1 for every 1∘C rise in temperature.
(i) Taking only the fundamental mode of the pipe, compute the beat frequency produced at 20∘C.
(ii) The temperature of the hall is then raised uniformly to 30∘C. Determine the new fundamental frequency of the pipe and the corresponding beat frequency with the same tuning fork.
(iii) Find the time interval between successive maxima of intensity at 30∘C.