Prove that even or odd harmonics …
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Posted by Aditya Gaur 6 years, 8 months ago
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Yogita Ingle 6 years, 8 months ago
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 + 1
Distance between two antinodes = λ / 2
l = P ( λ/2 )
λ = 2 I/P ----- (1)
n = V/λ ----- (2)
Substituting (2) in (1) we get,
n = PV / 2 l
P = 1, 2, 3 ...
P = 1; n1 = V/2l -- This is 1st harmonic frequency
P = 2; n2 = 2 V/2l = 2 n1 -- This is 2nd harmonic frequency
Hence n1:n2 = 1:2
Similarly, n1:n2:n3:n4 ... = 1:2:3:4...
Hence proved, in an open organ pipe both odd and even harmonic are produced.
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