(i) An organ pipe has one end closed and at the other end there is a vibrating diaphragm. The diaphragm is a pressure node. The pipe resonates when the frequency of the diaphragm is 2 KHz. Distance between adjacent nodes is 8.0 cm. When the frequency is slowly reduced, the pipe again resonates at 1.2 KHz.
(a) Find the length of the tube.
(b) Find the next frequency above 2 KHz at which the pipe resonates.
(ii) The figure shows an arrangement for measuring the speed of sound in air. A glass tube is fitted with a movable piston that allows the indicated length L to be adjusted. There is enough gap between the piston and the tube wall to allow the air to pass through it. A speaker is placed near the open end of the tube. A microphone is placed close to the speaker and it is connected to a waveform display. The display is a pure sinusoidal waveform making 750 oscillations in 5 s. Initially, the piston is held at end A and is then slowly pulled back. Loud sound is produced by the tube when `L = 50 cm` and `L = 157 cm`. Calculate the speed of sound in air.

Answer

(i) (a) 20 cm
(b) 2800 Hz
(ii) 321 m/s