In an open organ pipe, f₃ and f₆ are the 3rd and 6th harmonic frequencies respectively and f₆ − f₃ = 2200 Hz. Find the length of the pipe in mm.

Solution:

For an open organ pipe:

fₙ = nv / 2L

Therefore:

f₆ − f₃ = (6v / 2L) − (3v / 2L)

2200 = 3v / 2L

Taking speed of sound:

v = 330 m/s

2200 = (3 × 330) / 2L

2200 = 990 / 2L

4400L = 990

L = 990 / 4400

L = 0.225 m

L = 225 mm

Answer: 225 mm