An open organ pipe of length L resonates in its fundamental mode with a frequency f . If the pipe is lowered vertically into a tank of water such that exactly half of its length is submerged, what will be the new fundamental frequency of the air column? (Neglect end corrections)

Step-by-step solution

For an open organ pipe of length L , the fundamental frequency is given by: f = v 2L When the pipe is lowered vertically into water such that half of it is submerged, the water surface acts as a rigid boundary. The pipe now behaves as a closed organ pipe of length L' = L 2 . The fundamental frequency of this new closed pipe is: f' = v 4L' = v 4 ( L 2 ) = v 2L Comparing the two frequencies, we get f' = f . Answer: f