A closed organ pipe of length $l$ is sounded together with another closed organ pipe of length $l + x (x << l)$ both in fundamental mode. If $v$ = speed of sound, the beat frequency heard is
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${{\rm{f}}_{\rm{b}}} = \frac{{\rm{v}}}{{4l}} - \frac{{\rm{v}}}{{4(l + {\rm{x}})}}$
$ = \frac{v}{4}\left( {\frac{1}{l} - \frac{1}{{(l + {\rm{x}})}}} \right) = \frac{{\rm{v}}}{4}\left( {\frac{{l + {\rm{x}} - l}}{{l(l + {\rm{x}})}}} \right)$
$ \simeq \frac{{vx}}{{4{l^2}}}\quad $ ($\because$ $\;x < < l$)
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