MHT CET · Physics · Waves and Sound
A pipe \(\mathrm{P}_{\mathrm{C}}\) closed at one end and pipe \(\mathrm{P}_{\mathrm{O}}\) open at both ends are vibrating in second overtone. They are in resonance with a given tuning fork. The ratio of the length of pipe \(\mathrm{P}_{\mathrm{C}}\) vs \(\mathrm{P}_{\mathrm{O}}\) is (Neglect end correction)
- A \(\frac{4}{5}\)
- B \(\frac{5}{6}\)
- C \(\frac{2}{3}\)
- D \(\frac{3}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{5}{6}\)
Step-by-step Solution
Detailed explanation
For second overtone:
If they are in the resonance with the same tuning fork, using:
\(\lambda \mathrm{f}=\mathrm{v}\)
\(f\) and \(v\) are the same, so
\(\begin{aligned} & \lambda_C=\lambda_0 \\ & \therefore\left(\frac{4}{5} L_C\right)=\frac{2}{3} L_0 \\ & \Rightarrow \frac{L_C}{L_0}=\frac{5}{6}\end{aligned}\)
If they are in the resonance with the same tuning fork, using:
\(\lambda \mathrm{f}=\mathrm{v}\)
\(f\) and \(v\) are the same, so
\(\begin{aligned} & \lambda_C=\lambda_0 \\ & \therefore\left(\frac{4}{5} L_C\right)=\frac{2}{3} L_0 \\ & \Rightarrow \frac{L_C}{L_0}=\frac{5}{6}\end{aligned}\)
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