An organ pipe open at both ends is set into vibration.
(i) Explain the formation of stationary waves in such an air column and state the boundary conditions that must be satisfied at the two ends.
(ii) Using these boundary conditions, explain qualitatively why only wavelengths of the form λn=2L/n are allowed, where L is the length of the pipe and n is a positive integer.
(iii) Hence show that the corresponding frequencies are given by fn=nv/2L, where v is the speed of sound in air.
(iv) Draw neat, labelled sketches of the displacement profiles for the fundamental mode and the next two harmonics, clearly marking nodes and antinodes.