Q. The length of two open organ pipes are $l$ and $(l + \mathrm{\Delta}l)$ respectively. Neglecting end correction, the frequency of beats between them will be approximately

A) $\frac{v}{2l}$
B) $\frac{v}{4l}$
C) $\frac{v\mathrm{\Delta}l}{2l^{2}}$
D) $\frac{v\mathrm{\Delta}l}{l}$
Explanation

(c) $\lambda_{1} = 2l,\ \lambda_{2} = 2l + 2\Delta l \Rightarrow n_{1} = \frac{v}{2l}$and $n_{2} = \frac{v}{2l + 2\Delta l}$
$\Rightarrow No.\ of\ beats = n_{1} - n_{2} = \frac{v}{2}\left( \frac{1}{l} - \frac{1}{l + \Delta l} \right) = \frac{v\Delta l}{2l^{2}}$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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