A pipe open at both ends produces a fundamental frequency n₁ . When the pipe is kept with 3 4 ^ th of its length in water, it produces a note of fundamental frequency n₂ . The ratio of n₁ n₂ is

Step-by-step solution

A pipe of length L has fundamental frequency n₁ = v 2L when open at both ends. When 3 4 of the pipe is submerged in water, the remaining 1 4 L length of air column behaves as a closed pipe, with fundamental frequency n₂ = v 4 1 4 L = v L . The ratio of frequencies is therefore n₁ n₂ = v 2L v L = 1 2 . Final answer: D