Answer:
The power is [tex]P = 2.88*10^{-4 } \ W[/tex]
Explanation:
From the question we are told that
The distance from the siren is [tex]d = 17 \ m[/tex]
The intensity level is [tex]\beta = 49\ dB[/tex]
The threshold of hearing is [tex]I_0 = 1.0 *10^{-12} \ W/m^2[/tex]
Generally the intensity level is mathematically represented as
[tex]\beta = 10dB * log [\frac{I}{I_o} ][/tex]
Where I is the intensity at which the siren radiates the sound
substituting values
[tex]49 = 10 * log [\frac{I}{1.0 *10^{-12}} ][/tex]
=> [tex]I = 7.94*10^{-8} W/m^2[/tex]
Now the amount of power the siren put out is mathematically evaluated as
[tex]P= IA[/tex]
Where A is the area of the siren which is taken as a sphere and it is mathematically evaluated as
[tex]A = 4 \pi d^2[/tex]
So
[tex]P = I * 4 \pi d^2[/tex]
substituting values
[tex]P = 7.94 *10^{-8} * 4 * 3.142 * (17)^2[/tex]
[tex]P = 2.88*10^{-4 } \ W[/tex]
