Question
Two closed organ pipes, when sounded simultaneously gave $4$ beats per sec. If longer pipe has a length of $1m$. Then length of shorter pipe will be, ... $cm$ $(v = 300 m/s)$
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Answer
(b) For first pipe ${n_1} = \frac{v}{{4{l_1}}}$
and for second pipe ${n_2} = \frac{v}{{4{l_2}}}$
So, number of beats = ${n_2} - {n_1} = 4$
$ \Rightarrow $$4 = \frac{v}{4}\left( {\frac{1}{{{l_2}}} - \frac{1}{{{l_1}}}} \right)$
$ \Rightarrow $$16 = 300\left( {\frac{1}{{{l_2}}} - \frac{1}{1}} \right)$
$ \Rightarrow $${l_2} = 94.9$$cm$
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