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Prove that even or odd harmonics …

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

Yogita Ingle 6 years, 1 month 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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