Determine the fundamental, first overtone, and second overtone frequencies of an open organ pipe having a length of 20 cm . The speed of sound in air is 340 m s ⁻¹ .

Step-by-step solution

For an open organ pipe, the fundamental frequency is given by f₁ = v 2L Substituting the given values, v = 340 m s ⁻¹ and L = 20 cm = 0.2 m : f₁ = 340 2 0.2 = 340 0.4 = 850 Hz The first overtone corresponds to the second harmonic, f₂ = 2f₁ : f₂ = 2 850 = 1700 Hz The second overtone corresponds to the third harmonic, f₃ = 3f₁ : f₃ = 3 850 = 2550 Hz