The length of two open organ pipes are $l$ and $(l + \Delta l)$ respectively. Neglecting end correction, the frequency of beats between them will be approximately (Here $v$ is the speed of sound)
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(c) ${\lambda _1} = 2l,{\lambda _2} = 2l + 2\Delta l$
==> ${n_1} = \frac{v}{{2l}}$ and ${n_2} = \frac{v}{{2l + 2\Delta l}}$
==> 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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