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

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
Four open organ pipes of different lengths and different gases at same temperature as shown in figure. Let $f_A$, $f_B$, $f_C$ and $f_D$ be their fundamental frequencies then :[Take ${\gamma _{c{o_2}}} = 7/5$]
  • A
    $f_A/f_B =\sqrt 2 $
  • B
    $f_C/f_D = \sqrt {72/28}$
  • ✓
    $f_B/f_C =\sqrt {11/28}$
  • D
    $f_D/f_A =\sqrt {71/11}$
✓

Answer

Correct option: C.
$f_B/f_C =\sqrt {11/28}$
c
$f=\frac{\sqrt{\gamma R T}}{2 L \sqrt{M}}=\frac{k}{L \sqrt{M}}, f_{A}=\frac{k}{L \sqrt{2}}$

$f_{B}=\frac{2 k}{L \sqrt{32}}, f_{c}=\frac{3 k}{2 L \sqrt{28}}$

$f_{D}=\frac{3 k}{L \sqrt{44}}, \therefore f_{C} / f_{D}=\sqrt{\frac{11}{28}}$

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