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14. waves and sound — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
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)
  • A
    $\frac{v}{{2l}}$
  • B
    $\frac{v}{{4l}}$
  • ✓
    $\frac{{v\Delta l}}{{2{l^2}}}$
  • D
    $\frac{{v\Delta l}}{l}$
✓

Answer

Correct option: C.
$\frac{{v\Delta l}}{{2{l^2}}}$
c
(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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