A closed organ pipe and an open organ pipe have their first overtones identical in frequency . Their lenghts are in the ratio

Options

A. ` 1 : 2`
B. ` 2 : 3`
C. ` 3 : 4`
D. ` 4 : 5`

Answer

C

Explanation

For the closed pipe , `n = V/(4L_(1)) " and " 3n = (3V)/(4 L_(1))`
For the open pipe, `n_(1) = V/(2L_(2)) " and " 2n_(1) = V/L_(2) `
As `3n = 2n _(1) :. (3V)/(4L_(1)) = V/L_(2) :. 4L_(1) = 3L_(2) `
` :. L_(1).L_(2) = 3/4 `