show that for a clósed organ pipe only odd harmonics are present wheras for an open organ pipe all the harmonics are present​

For a closed organ pipe, the point at the closed end is always a node, 'N' while the open end is always an antinode, 'A'

Therefore, for a closed organ pipe, we only have;

NA = N↔A = First harmonics = f₁

NANA = NA↔AN↔ NA = Third harmonics, = f₃ = 3·f₁

NANANA = NA↔AN ↔ NA ↔ AN ↔ NA = f₅ = 5·f₁

It can also be shown that for a closed organ pipe, only f₇, f₉, f₁₁, ... are present

Therefore, a closed organ pipe has only odd harmonics present

For an open organ pipe, we have;

ANA = First harmonics = f₁

ANANA = ANA ↔ ANA = Second harmonics = f₂ = 2·f₁

ANANANA = ANA ↔ ANA ↔ ANA = Third harmonics = f₃ = 3·f₁

Similar relationship exist for f₄, f₅, f₆...

Therefore, for an open organ pipe, all harmonics, (multiples of the fundamental, f₁) are present

Explanation:

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explanation:

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