physics PLEASE HELP
posted by Anonymous .
A source emits sound uniformly in all directions. There are no reflections of the sound. At a distance r1 from the source the sound is 6.5 dB louder than it is at a distance r2 from the source. What is the ratio r1/r2?

The difference in decibels between the two is defined to be
10 * log (P2/P1)
Where the log function is in base 10, and P2 and P1 are the power of the sources at r2 and r1
6.5 = 10*log(P2/P1)
0.65 = log(P2/P1)
10^0.65 = P2/P1 = 4.46
Power is proportional to the radius squared, so P2/P1 = (r2/r1)^2
r2/r1 = 4.46^(0.5) = 2.11
r1/r2 = 2.11^1 = 0.47