(i) Two cylindrical pipes are each of length `L = 30 cm`. One of them contains hydrogen and the other has oxygen at the same temperature. The ends A, B, C and D of the pipes are fitted with flexible diaphragms. The diaphragms A and C are set into oscillations simultaneously using the same source having frequency `f = 600 Hz`. Calculate the difference in phase of oscillations of the diaphragms D and B if it is known that the speed of sound in hydrogen at the temperature concerned is `1200 m//s`.

(ii) The air column in a pipe closed at one end is made to vibrate in its second overtone by a tuning fork of frequency `440 Hz`. The speed of sound in air is `330 m//s`. `P_(0)` is mean pressure in the pipe and `DeltaP_(0)` is maximum amplitude of pressure variation. Neglect end correction.
(a) Find the length L of air column.
(b) What is amplitude of pressure variation at the middle of the column?
(c) What is maximum and minimum pressure at the closed end?

Answer

(i) `0.9 pi` rad
(ii) (a) 93.75cm
(b) `(DeltaP_(0))/sqrt(2)`
(c) `P_("max")=P_(0)+DeltaP_(0); P_("min")=P_(0)-DeltaP_(0)`