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A closed organ pipe of radiusr(1) and an...

A closed organ pipe of radius`r_(1)` and an open organ pipe of radius `r_(2)` and having same length 'L' resonate when exited with a given tuning fork. Closed organ pipe and open organ pipe resonates in fundamental mode, then :

A

`1.2 (r_(2)-r_(1)) =L`

B

`r_(2)-r_(1)=L`

C

`r_(2)-2r_(1) = 2.5L`

D

`2r_(2)-r_(1) = 2.5L`

Text Solution

Verified by Experts

The correct Answer is:
A
With end correction for closed organ pipe
`implies (lambda)/4 = L+e`
and for open organ pipe `(lambda)/2 = L + 2e_(2)`
SO `4(L+e_(1))=2(L+2e_(2))`
Now, `e_(1) = 0.6 r_(1)`
and `e_(2) = 0.6 r_(2)`
`2L = 4(e_(2)-e_(1))`
`L = 2(e_(2)-e_(1))`
`=2 xx 0.6 (r_(2)-r_(1))`
`L = 1.2 (r_(2)-r_(1))`.
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