A closed organ pipe of radius `r_(1)` and an open organ pipe of radius `r_(2)` both having same length 'L' resonate when excited with a given tunning fork. Closed organ pipe resonates in its fundamental mode where as open organ pipe resonates in its overtone , then

Options

A. `r_(2) - r_(1) = L`
B. `r_(2) = r_(1) = L//2`
C. `r_(2) - 2r_(1) = 2.5 L`
D. `2r_(2) - r_(1) = 2.5 L`

Answer

C

Explanation

`(lamda)/(4)=L+0.6 r_(1)`
`lamda = L + 1.2 r_(1)`
`rArr 4(L+0.6 r_(1))=(L+1.2r_(2))rArr r_(2)-2r_(1)=2.5L`