In an open organ pipe ₃ and ₆ are 3^ rd and 6^ th harmonic frequencies, respectively. If ₆- ₃=2200 ~Hz then length of the pipe is _ _ _ _ mm . (Take velocity of sound in air is 330 ~m / s .)

Step-by-step solution

For an open organ pipe, the n -th harmonic frequency is f_n = n v 2L . The 3rd harmonic is v₃ = 3 330 2L and the 6th harmonic is v₆ = 6 330 2L . Taking the difference: v₆ - v₃ = (6-3) 330 2L = 3 330 2L = 2200 . Solving for L : L = 3 330 2 2200 = 990 4400 = 0.225 m = 225 mm.