A rocket in a fireworks display explodes high in the air. The sound spreads out uniformly in all directions. The intensity of the sound is 1.90 10-6 W/m2 at a distance of 120 m from the explosion. Find the distance from the source at which the intensity is 0.80 10−6 W/m2.

Question

A rocket in a fireworks display explodes high in the air. The sound spreads out uniformly in all directions. The intensity of the sound is 1.90  10-6 W/m2 at a distance of 120 m from the explosion. Find the distance from the source at which the intensity is 0.80  10−6 W/m2.

algebra · Answer

If I1 is the intensity at a distance 150 m from the source and I2 is the intensity at a distance of d m from the source ,

I1 *150^2 = I2 *d^2

d^2 =[ I1 / I2 ]*150^2

[I1 / I2] = 1.9 /0.8= 2.375

d^2 = 2.375*150^2

d =231.17 m.