Question

Prove that in an open organ pipe both odd and even harmonic are produced

Answer 1

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 + 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.