Question

Find the intensity of an 89 dB sound.  What happens to this intensity if you move 4 times the distance away (actually need a value)? What is the dB reading of this new intensity?

Answer 1

1)

$$89=10\lg\frac{I}{10^{-12}}\\I=0.000794\frac{W}{m^2}$$

2)

$$I'=\frac{1}{4^2}I=\frac{1}{4^2}0.000794=0.000049625\frac{W}{m^2}$$

$$\beta'=10\lg\frac{0.000049625}{10^{-12}}=77\ dB$$