TS EAMCET · Physics · Waves and Sound
An organ pipe \(P_1\), closed at one end and containing a gas of density \(\rho_1\) is vibrating in its first harmonic. Another organ pipe \(P_2\), open at both ends and containing a gas of density \(\rho_2\) is vibrating in its third harmonic. Both the pipes are in resonance with a given tuning fork. If the compressibility of gases is equal in both pipes, the ratio of the lengths of \(P_1\) and \(P_2\) is (assume the given gases to be monoatomic)
- A \(\frac{1}{3}\)
- B 3
- C \(\frac{1}{6} \sqrt{\frac{\rho_1}{\rho_2}}\)
- D \(\frac{1}{6} \sqrt{\frac{\rho_2}{\rho_1}}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{6} \sqrt{\frac{\rho_2}{\rho_1}}\)
Step-by-step Solution
Detailed explanation
Frequency of closed organ pipe for first harmonic \(n_1=\frac{v_1}{4 l_1}\). Frequency of open organ pipe for third harmonic \(n_3=\frac{3 v_2}{2 l_2}\) At resonance, \(\quad n_1=n_3\) or \(\quad \frac{v_1}{4 l_1}=\frac{3 v_2}{2 l_2}\) or…
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