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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 ${P_1}$ closed at one end vibrating in its first overtone and another pipe ${P_2}$ open at both ends vibrating in its third overtone are in resonance with a given tuning fork. The ratio of lengths of ${P_1}$ and ${P_2}$ is
  • A
    $1:2$
  • B
    $1:3$
  • ✓
    $3:8$
  • D
    $3:4$
✓

Answer

Correct option: C.
$3:8$
c
(c) First overtone of closed organ pipe ${n_1} = \frac{{3v}}{{4{l_1}}}$
Third overtone of open organ pipe ${n_2} = \frac{{4v}}{{2{L_2}}}$
${n_1} = {n_2}$ (Given)

$ \Rightarrow $$\frac{{3v}}{{4{L_1}}} = \frac{{4v}}{{2{L_2}}} \Rightarrow $$\frac{{{L_1}}}{{{L_2}}} = \frac{3}{8}$

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