An open organ pipe has a fundamental frequency f . It is dipped vertically into a drum of water until its fundamental frequency becomes 1.5f . What fraction of the pipe's total length is submerged in the water?

Step-by-step solution

Let the total length of the open pipe be L . The fundamental frequency of the open pipe is given by: f = v 2L When the pipe is partially dipped in water, it behaves as a closed organ pipe. Let the length of the air column remaining above the water be x . The new fundamental frequency is: f' = v 4x We are given that the new frequency is 1.5f , which can be written as 3 2 f . Substituting the value of f : v 4x = 3 2 ( v 2L ) v 4x = 3v 4L Solving for x , we get: x = L 3 This is the length of the air column. The length