A source of sound operates at 2.0 kHz and 20 W , radiating sound uniformly in all directions. Given that the speed of sound in air is 340 m s ⁻¹ and the density of air is 1.2 kg m ⁻³ , what is the pressure amplitude at a distance of 6.0 m from the source?

Step-by-step solution

Intensity of sound at a distance r from a point source is given by I = P 4 r^2 The relation between intensity and pressure amplitude p_m is I = p_m^2 2 v Equating the two expressions for intensity: P 4 r^2 = p_m^2 2 v p_m = P v 2 r^2 Substituting the given values P = 20 W , = 1.2 kg m ⁻³ , v = 340 m s ⁻¹ , and r = 6.0 m : p_m = 20 1.2 340 2 (6.0)^2 p_m = 8160 72 p_m = 340 3 Using 3.14 : p_m 36.07 6.0 Pa