The length of two open organ pipes are l and $(1 + \Delta l)$ respectively. Neglecting end correction, the frequency of beats between them will be approximately (Here v is the speed of sound)
$(a) \frac{v}{2l} (b) \frac{v}{4l} (c) \frac{v \Delta l}{2 l^{2}} (d) \frac{v \Delta l}{l}$
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$\lambda_{1} = 2l, \lambda_{2} = 2l + 2\Delta l$
$\Rightarrow n_1 = \frac{v}{2l} \text{ and } n_2 = \frac{v}{2l+2\Delta l}$ $\Rightarrow \text{No. of beats} = n_1 - n_2 = \frac{v}{2} \left( \frac{1}{l} - \frac{1}{l+\Delta l} \right) = \frac{v \Delta l}{2 l^2}$
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