Question

Approximately how many times louder is a 145-dB sound than a 85-dub sound?

Answer 1

For the 145-dB-sound:

$$L_1=10\log_{10}\frac{P_1}{P_0}\space\rightarrow P_1=10^{L_1/10}P_0,$$

for the 85-dB-sound:

$$L_2=10\log_{10}\frac{P_2}{P_0}\space\rightarrow P_2=10^{L_2/10}P_0.$$

Find the ratio:

$$\frac{P_1}{P_2}=10^{(L_1/10-L_2/10)}=10^6.$$