In the resonance tube experiment , the first resonance is heard when length of air column is `l_(1)` and second resonance is heard when length of air column is `l_(2)`. What should be the minimum length of the tube so that third resonance can also be heard.

Options

A. `2 l_(2) - l_(1)`
B. `2 l_(1)`
C. `5 l_(1)`
D. `7 l_(1)`

Answer

A

Explanation

`l_(1) + epsilon = (v)/( 4 f_(0))`
`l_(2) + epsilon = ( 3 v)/( 4 f_(0))`
`l_(13 + epsilon = ( 5 v)/( 4 f_(0))`
On solving , we get `l_(3) = 2l_(2) - l_(1)`