JEE Mains · Physics · STD 11 - 14. waves and sound
A closed organ pipe of length \(L\) and an open organ pipe contain gases of densities \(\rho_{1}\) and \(\rho_{2}\) respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is \(\frac{ x }{3} L \sqrt{\frac{\rho_{1}}{\rho_{2}}}\) where \(x\) is ......... . (Round off to the Nearest Integer)
- A \(4\)
- B \(6\)
- C \(2\)
- D \(1\)
Answer & Solution
Correct Answer
(A) \(4\)
Step-by-step Solution
Detailed explanation
\(f_{c}=f_{0}\) \(\frac{3 V_{C}}{4 L}=\frac{2 V_{0}}{2 L^{\prime}}\) \(\frac{3 V_{C}}{4 L}=\frac{V_{0}}{L^{\prime}}\) \(L ^{\prime}=\frac{4 L }{3} \frac{ V _{0}}{ V _{ C }}=\frac{4 L }{3} \sqrt{\frac{ B \cdot \rho_{1}}{\rho_{2} \cdot B }}( B\) is bulk modulus)…
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