An organ pipe closed at one end has a fundamental frequency ₀ . The cap at the closed end is then removed, making it a pipe open at both ends, and the pipe is cut into two equal halves. The fundamental frequency of one of these open halves is :

Step-by-step solution

Let the length of the original pipe be L and the speed of sound be v . The fundamental frequency of the pipe closed at one end is given by: ₀ = v 4L When the cap is removed, the pipe becomes open at both ends. It is then cut into two equal halves, so the length of each half is L' = L 2 . The fundamental frequency of an open pipe of length L' is: ' = v 2L' Substituting L' = L 2 : ' = v 2 ( L 2 ) = v L From the first equation, we have v L = 4 ₀ . Therefore, ' = 4 ₀ . Answer: 4 ₀