Prove that even or odd harmonics are produced in open organ pipe

1.	Prove that even or odd harmonics are produced in open organ pipe
Answer» If conditions at the two boundaries are same, then both even and odd harmonics are obtained. Based on this principle, in an open organ pipe both odd and even harmonic are produced.In Pth harmonic,Total anti-nodes between two open ends = P + 1Distance between two antinodes = λ / 2l = P ( λ/2 )λ = 2 I/P ----- (1)n = V/λ ----- (2)Substituting (2) in (1) we get,n = PV / 2 lP = 1, 2, 3 ...P = 1; n1 = V/2l -- This is 1st harmonic frequencyP = 2; n2 = 2 V/2l = 2 n1 -- This is 2nd harmonic frequencyHence n1:n2 = 1:2Similarly, n1:n2:n3:n4 ... = 1:2:3:4...Hence proved, in an open organ pipe both odd and even harmonic are produced.\xa0

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