An organ pipe of length 66cm is open at both ends. The speed of sound in air is 330ms−1. Study the pipe under the following conditions:
(a) Sketch the displacement curve for the fundamental mode, clearly indicating nodes and antinodes along the pipe length.
(b) Using the condition for displacement antinodes at both ends, derive an expression that relates the pipe length L to the wavelength of the fundamental mode.
(c) Calculate the fundamental frequency of the pipe.
(d) The pipe is then sounded in its second overtone (third harmonic). Determine the wavelength and the corresponding frequency.
(e) If the temperature rises so that the speed of sound becomes 336ms−1, find the percentage change in the fundamental frequency.