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A pipe open at both ends has a fundamental frequency f in air. The pipe is dipped vertically into water until exactly half its length is submerged. What is the fundamental frequency of the air column now?

1. f
2. f / 2
3. 3f / 4
4. 2f

Correct answer: f

Solution

Original open pipe of length L: f = v/(2L). After dipping half in water, the air column is L/2 with one closed end (water surface) and one open end. For a closed pipe of length L/2: fundamental frequency f' = v/(4*(L/2)) = v/(2L) = f. The frequency remains unchanged.

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