Sound waves physics question

Question

A trainer's automatic machine creates sounds as the K-9 dog approaches. The sound can just be heard at a level of 68 dB by the K-9 dog 0.25 km away.

1. What is the average power generated by the machine?

1. What intensity level of the machine's sound is heard by the K-9 dog at 0.25 km away?

Answer 1

Let's answer the second question first: 68 dB = (10dB) • log (I/I_o), I_o = 1 x 10^-12 W/m², log (I/I_o) = 6.8, I/I_o = 10^6.8 = 6.31 x 10⁶, I = 6.31 x 10^-6 W/m².

First question: I = P/4π r² so Power at distance 250 m is P = 4π (250 m)² (6.31 x 10^-6 W/m²) = 5.0 Watts (2 sig figs).