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Organ Pipes & Resonance Tube question from JEE Main 2016

Q110JEE Main 2016Easy

Organ Pipes & Resonance Tube

A pipe open at both ends has a fundamental frequency $f$ in air. The pipe is dipped vertically in water so that half of it is in water. The fundamental frequency of the air column is now:

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Answer: (b)

Open pipe: $f = \frac{v}{2L}$ .
Half in water leaves a closed pipe of length $\frac{L}{2}$ : $f' = \frac{v}{4(L/2)} = \frac{v}{2L}$ .
So the answer is (b) $f$ .

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