question_answer

If \[{{\ell }_{1}}\]and \[{{\ell }_{2}}\]are the length of an column for the first and second Resonance when a turning fork of frequency n is sounded on a resonance tube, then the distance of the anti-node from the top end of the resonance tube is

A) \[2({{\ell }_{1}}-{{\ell }_{1}})\]      

B)      \[\frac{1}{2}(2{{\ell }_{1}}-{{\ell }_{2}})\]

C)      \[\frac{{{\ell }_{2}}-3{{\ell }_{1}}}{2}\]    

D)      \[\frac{{{\ell }_{1}}-{{\ell }_{2}}}{2}\]                  

Correct Answer: C

Solution :

\[{{\ell }_{1}}+x=\lambda /4\] \[{{\ell }_{2}}+x=\frac{3\lambda }{4}\] \[\Rightarrow \]\[x=\frac{{{\ell }_{2}}-3{{\ell }_{1}}}{2}\] Hence, the correction option is [c].