An open organ pipe of length L is sounding its 2^ nd overtone. It is then dipped vertically in water such that exactly half of its length is submerged. The air column above the water is now made to vibrate in its 2^ nd overtone. The ratio of the new frequency to the original frequency is:

Step-by-step solution

For an open organ pipe, the n^ th overtone corresponds to the (n+1)^ th harmonic. The 2^ nd overtone is the 3^ rd harmonic. The original frequency f₁ is: f₁ = 3v 2L When the pipe is dipped vertically in water such that half of it is submerged, it becomes a closed organ pipe of length L' = L 2 . For a closed organ pipe, the n^ th overtone corresponds to the (2n+1)^ th harmonic. The 2^ nd overtone is the 5^ th harmonic. The new frequency f₂ is: f₂ = 5v 4L' = 5v 4 ( L 2 ) = 5v 2L The ratio of the new frequency to the