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 intensity at a distance of 6.0 m from the source?

Step-by-step solution

The intensity of sound at a distance r from a point source radiating uniformly in all directions is given by the power divided by the surface area of a sphere of radius r . I = P 4 r^2 Given: Power of the source, P = 20 W Distance, r = 6.0 m Substituting the values into the formula: I = 20 4 (6.0)^2 I = 20 4 36 I = 5 36 W m ⁻² Using 3.14 : I 5 113.04 W m ⁻² I 0.0442 W m ⁻² I 44 mW m ⁻² The frequency, speed of sound, and density of air are extra information not required for this calculation.