Question

P2.8 A tuning fork is struck generating a sound which results in a 22nd harmonic standing wave in a 90cm tube which is open at both ends. This same tuning fork simultaneously creates a 19th harmonic standing wave in a tube which is closed at one end. Determine the length of the closed tube.

Answer 1

From given data, * In a 22^nd harmonic standing wave in a 90 cm tube which is open at both ends. * This same tuning fork simultaneously creates a 19^th harmonic standing wave in a tube which is closed at one end. * Let us consider the relation for the standing wave when open at both ends is f_n = nv/2L Where n = 22 L = 90 cm Consider another formula for tube closed at one end. F_n = (2n' - 1) v/4 L_1 Where, n' = 19 Since the tuning fork is same, hence these two equations are same as thus, \r\n nv/2L = (2n' - 1) v/4L_1 22/2 (90) = [2(19) - 1]/4L' 0.122 = 37/4L' L' = 75.82 cm leftdoublearrow This is the length of the tube.

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