Question

What is the decibel level of the radio with intensity 10−7 watts per square inch? Use a logarithmic model to solve.

Answer 1

`D = 50`

Explanation:

Given

`I = 10^(-7)W/m^2` --- Intensity

Required

Determine the decibel level (D)

This is calculated as:

`D = 10 * log((I)/(I_n))`

Where:

`I_n =` The threshold intensity

`I_n =1 * 10^(-12)W/m^2`

So, we have:

`D = 10 * log((I)/(I_n))`

This gives:

`D = 10 * log((10^(-7)W/m^2)/(1 * 10^(-12)W/m^2))`

`D = 10 * log((10^(-7))/(10^(-12)))`

Apply law of indices

`D = 10 * log(10^(-7--12))`

`D = 10 * log(10^(5))`

Apply law of logarithm

`loga^b = b\ log(a)`

So, we have:

`D = 10 * 5 * log(10)`

`log(10) =1`

So:

`D = 10 * 5 *1`

`D = 50`

Hence, the decibel level is 50