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

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
A closed organ pipe and an open organ pipe have their first overtones identical in frequency. Their length are in the ratio
  • A
    $1:2$
  • ✓
    $3:4$
  • C
    $4:5$
  • D
    $2:3$
✓

Answer

Correct option: B.
$3:4$
b
$f_{e}=\frac{(2 m+1) V}{4 L_{c}}$

${f_o} = \frac{{(m + 1)V}}{{2{L_o}}}$

For ${\rm{m}} = 1$ ( ${{1^{{\rm{st }}}}}$ overtone)

$\mathrm{f}_{\mathrm{c}}=\mathrm{f}_{\mathrm{o}}$

$\frac{{3{\text{V}}}}{{4{{\text{L}}_c}}} = \frac{{2{\text{V}}}}{{2{{\text{L}}_o}}}\quad  \Rightarrow \quad \boxed{\frac{{{{\text{L}}_c}}}{{{{\text{L}}_o}}} = \frac{3}{4}}$

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