If the distance from a bugle is tripled, by what factor does the sound intensity decrease? Assume that no reflections affect the sound.

Solution 27E Step 1: The intensity of the sound waves and the distance is related by the mathematical equation, 2 I = P / 4 r Where, P - Power generated by the source of sound r - Distance which it travels. So, the only thing which will influence the intensity will be the distance “r”. 2 We can write, I 1 / r -------------------- (1) If the distance is tripled, then the distance will become 3r. 2 The intensity will be, I ’ 1 / (3r) 2 I’ 1 / 9r -------------------- (2) Divide equation 2 by 1 we get, 2 2 I’ / I = (1/9r )/(1/r ) = 1/9 Rearranging the equation we get, I’ = I /9 Conclusion: The intensity of the sound will be decreased 1/9th of the initial value if distance is tripled.