(a) Draw the stationary wave patterns for the first three resonant modes of
(i) an air column closed at one end and
(ii) an air column open at both ends.
(b) Using the sketches in part (a), explain clearly why only alternate (odd-numbered) harmonics are possible for the closed pipe, whereas every harmonic is possible for the open pipe.
(c) Starting from the condition for a standing wave in an air column, derive the general expression for the frequency of the nth harmonic for:
(i) the closed pipe,
(ii) the open pipe.
(d) Compare the fundamental frequencies of two pipes of equal length, one closed at one end and the other open at both ends. State which one is higher and by what factor.