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

Gujarat BoardEnglish MediumSTD 11 SciencePhysics14. waves and sound1 Mark
MCQ
In an experiment to determine the velocity of sound in air at room temperature using a resonance is observed when the air column has a length of $20.0 \,cm$ for a tuning fork of frequency $400 \,Hz$ is used. The velocity of the sound at room temperature is $336 \,ms ^{-1}$. The third resonance is observed when the air column has a length of ......... $cm$
  • A
    $103$
  • B
    $100$
  • C
    $110$
  • ✓
    $104$
✓

Answer

Correct option: D.
$104$
d
For first resonance

$\ell_{1}+ e =\frac{\lambda}{4}$

$\lambda=\frac{336}{400} \times 100 \,cm =84 \,cm \Rightarrow \frac{\lambda}{4}=21 \,cm$

$e =21-20=1 \,cm$

For third resonance

$\ell_{3}+ e =\frac{5 \lambda}{4}=105 \,cm \Rightarrow \ell_{3}=104 \,cm$

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