Two stereo speakers are separated by a distance of 2.40 m . A person stands at a distance of 3.20 m directly in front of one of the speakers, as shown in the figure. Determine the frequencies in the audible range ( 20 – 2000 Hz ) for which the listener will hear a minimum sound intensity. The speed of sound in air is 320 m s ⁻¹ .

Step-by-step solution

Let the two speakers be S₁ and S₂ , and the listener be at point P . The distance from the first speaker to the listener is: L₁ = 3.20 m The distance from the second speaker to the listener is: L₂ = (2.40)^2 + (3.20)^2 = 5.76 + 10.24 = 16.00 = 4.00 m The path difference x between the sound waves reaching the listener is: x = L₂ - L₁ = 4.00 - 3.20 = 0.80 m For minimum sound intensity (destructive interference), the path difference must be an odd multiple of half the wavelength: x = (2n + 1) 2 , where n = 0, 1, 2, Us