A) \[{{n}_{0}}\Delta \ell /\ell \]
B) \[8{{n}_{0}}\Delta \ell /\ell \]
C) \[2{{n}_{0}}\Delta \ell /\ell \]
D) \[{{n}_{0}}\Delta \ell /2\ell \]
Correct Answer: B
Solution :
\[{{n}_{0}}=\frac{v}{2\ell },{{n}_{1}}=\frac{v}{2(\ell /2-\Delta \ell )},{{n}_{2}}=\frac{v}{2(\ell /2+\Delta \ell )}\] Beat frequency \[={{n}_{1}}-{{n}_{2}}\] \[\Rightarrow \] \[v\left[ \frac{1}{\ell -2\Delta \ell }-\frac{1}{\ell +2\Delta \ell } \right]\] \[=v\left[ \frac{(\ell +2\Delta \ell )-(\ell -2\Delta \ell )}{{{\ell }^{2}}-4\Delta {{\ell }^{2}}} \right]\] \[=v\frac{4\Delta \ell }{{{\ell }^{2}}-4\Delta {{\ell }^{2}}}=\frac{8}{\ell }\frac{\Delta \ell v}{2{{\ell }^{2}}}=\frac{8\Delta \ell {{n}_{0}}}{\ell }\]You need to login to perform this action.
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