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n th harmonic of a closed organ is equal...

`n th` harmonic of a closed organ is equal to `m th` harmonic of an pipe . First overtone frequency of the closed organ pipe is also equal to first overtone frequaency of an organ pipe . Find the value of `n`, if `m = 6`.

Text Solution

Verified by Experts

The correct Answer is:
`9`
`n((V)/( 4 L_(c ))) = m ((V)/( 2L_(0)))` `(i)`
Also `3((V)/( 4L_( c))) = 2 ((V)/( 2 L_(0)))` `(ii)`
FromEq. (ii) `(L_(c))/(L_(0)) = (3)/(4)`
From Eq.(i) ` (n)/(m) = 2((L_(c ))/(L_(0))) = (6)/(4) = (3)/(2) = (9)/(6)`
`n = 9` if `m = 6`
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