In Quincke's experiment, the sound intensity exhibits a minimum value I at a specific position. When the sliding tube is pulled out by a distance of 16.5 mm , the intensity rises to a maximum of 9 I . Taking the speed of sound in air as 330 m s ⁻¹ , determine the ratio of the amplitudes of the two waves arriving at the detector, assuming this ratio remains largely unchanged between the positions of minimum and maximu

Step-by-step solution

The minimum intensity is given as I_ min = I and the maximum intensity is I_ max = 9I . The intensity of sound is proportional to the square of its amplitude. For two waves of amplitudes A₁ and A₂ , the maximum and minimum intensities are given by: I_ max = k(A₁ + A₂)^2 I_ min = k(A₁ - A₂)^2 Taking the ratio of the maximum to minimum intensity: I_ max I_ min = (A₁ + A₂)^2 (A₁ - A₂)^2 = 9I I = 9 Taking the square root of both sides: A₁ + A₂ A₁ - A₂ = 3 Cross-multiplying yields: A₁ + A₂ = 3A₁ - 3A₂ 4A₂ = 2A₁ A₁ A₂ =