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

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
An organ pipe open at one end is vibrating in first overtone and is in resonance with another pipe open at both ends and vibrating in third harmonic. The ratio of length of two pipes is
  • ✓
    $1:2$
  • B
    $4:1$
  • C
    $8:3$
  • D
    $3:8$
✓

Answer

Correct option: A.
$1:2$
a
(a) In first overtone of organ pipe open at one end,

end, ${n_c} = \frac{{3v}}{{4{l_c}}}$.....$(i)$

Third harmonic or second overtone of organ pipe open at both end,

${n_0} = \frac{{3v}}{{2{l_0}}}$.....$(ii)$

given ${n_c} = {n_o}$

$ \Rightarrow \,\,\,\,\frac{{3v}}{{4{l_c}}} = \frac{{3{v_0}}}{{2{l_0}}}\,\,\,$

$\Rightarrow \,\,\frac{{{l_c}}}{{{l_o}}} = \frac{1}{2}.$

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