Consider an air column of length L that is closed at one end and open at the other.
(i) Starting from the conditions that must be satisfied at the two ends, derive an expression for the wavelength and the corresponding frequency of the n-th harmonic that can exist in this pipe.
(ii) Hence obtain the ratio of the frequencies of the first, second and third allowed harmonics in such a pipe.
(iii) An open pipe of length L1 has the same fundamental frequency as the closed pipe of length L. Establish the relation between L1 and L.