If `l_1 and l_2` are the lengths of air column for two air column for two consecutive resonance position when a turning fork of frequency f is sounded in a resonance tube, then end correction is :

Options

A. `((l_2-3l_1))/2`
B. `((l_2+3l_1))/2`
C. `((l_2+l_1))/2`
D. `((3l_2-l_1))/4`

Explanation

`V/(4(l_1+e))=f, (3V)/(4(l_2+e))=f`
`V/(4f)=l_1+e`
`(3V)/(4f)=l_2+e`
`(2V)/(4f)=l_2-l_1=V=2f(l_2-l_1)`
`e=(2f(l_2-l_1))/(4f)-l_1=(2l_2-2l_1-4l_1)/4=(2(l_2-3l_1))/4`