Question

Sound is measured in decibels, using the formula d = 10 log() where P is the intensity of the sound and P, is the weakest sound the human ear can hear. A horn has a decibel warning of20. How many times more intense is this horn compared to the weakest sound heard to the human ear?

Answer 1

We have the following:

The formula is the following

`d=10\log ((P)/(P_o))`

From what the statement tells us, the value of d is equal to 20, now we replace and solving for P / Po

`\begin{gathered} 10\log ((P)/(P_o))=20 \\ (10)/(10)\log ((P)/(P_o))=(20)/(10) \\ \log ((P)/(P_o))=2\rightarrow\log (x)=2\rightarrow x=10^2\rightarrow x=100 \\ (P)/(P_o)=100 \\ P=100\cdot P_o \end{gathered}`

Therefore, the sound of the horn is about 100 more intense than the weakest sound heard to the human ear.