Answered

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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?

Sagot :

We have the following:

The formula is the following

[tex]d=10\log (\frac{P}{P_o})[/tex]

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

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

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

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