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NEET 2022
Exam
NEET
Year
2022
Subject
Physics
Chapter
Waves and Sound

NEET 2022 · Physics · Waves and Sound

An organ pipe filled with a gas at 27^ C resonates at 400 ~Hz in...

An organ pipe filled with a gas at 27∘C27^{\circ} \mathrm{C} resonates at 400 Hz400 \mathrm{~Hz} in its fundamental mode. If it is filled with the same gas at 90∘C90^{\circ} \mathrm{C}, the resonance frequency at the same mode will be:

Options

  1. A420 Hz420 \mathrm{~Hz}
  2. B440 Hz440 \mathrm{~Hz}
  3. C484 Hz484 \mathrm{~Hz}
  4. D512 Hz512 \mathrm{~Hz}

Correct answer

B. 440 Hz440 \mathrm{~Hz}

Step-by-step solution

As per question, we have; frequency, f=v4lf=\frac{v}{4 l} Hence, ⇒4lf2=v1v2⇒400f2=T1 T2⇒400f2=300363⇒[∵V∝T]⇒f2=363300×400⇒f2=440 Hz\begin{array}{l} \Rightarrow \frac{4 l}{f_2} =\frac{v_1}{v_2} \\ \Rightarrow \frac{400}{f_2} =\sqrt{\frac{\mathrm{T}_1}{\mathrm{~T}_2}} \\ \Rightarrow \frac{400}{f_2} =\sqrt{\frac{300}{363}} \\ \Rightarrow [\because \mathrm{V} \propto \sqrt{\mathrm{T}}] \\ \Rightarrow f_2 =\sqrt{\frac{363}{300}} \times 400 \\ \Rightarrow f_2 =440 \mathrm{~Hz} \end{array}
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