An air column may resonate either as an organ pipe open at both ends or as an organ pipe closed at one end. Answer the following questions with reference to a pipe of length L.
(i) Draw labelled sketches of the displacement–distance profiles for the fundamental mode and the first two overtones for:
(a) a pipe open at both ends, and
(b) a pipe closed at one end.
(ii) For each mode drawn in part (i), state the corresponding harmonic number n.
(iii) Explain, with the aid of the sketches, why only odd harmonics are present when the pipe is closed at one end.
(iv) Show that the fundamental frequency of a pipe open at both ends is twice the fundamental frequency of a pipe of identical length that is closed at one end.