Answer:
[tex]D = 50[/tex]
Step-by-step explanation:
Given
[tex]I = 10^{-7}W/m^2[/tex] --- Intensity
Required
Determine the decibel level (D)
This is calculated as:
[tex]D = 10 * log(\frac{I}{I_n})[/tex]
Where:
[tex]I_n =[/tex] The threshold intensity
[tex]I_n =1 * 10^{-12}W/m^2[/tex]
So, we have:
[tex]D = 10 * log(\frac{I}{I_n})[/tex]
This gives:
[tex]D = 10 * log(\frac{10^{-7}W/m^2}{1 * 10^{-12}W/m^2})[/tex]
[tex]D = 10 * log(\frac{10^{-7}}{10^{-12}})[/tex]
Apply law of indices
[tex]D = 10 * log(10^{-7--12})[/tex]
[tex]D = 10 * log(10^{5})[/tex]
Apply law of logarithm
[tex]loga^b = b\ log(a)[/tex]
So, we have:
[tex]D = 10 * 5 * log(10)[/tex]
[tex]log(10) =1[/tex]
So:
[tex]D = 10 * 5 *1[/tex]
[tex]D = 50[/tex]
Hence, the decibel level is 50
