Answer:
about 9.93 W
Explanation:
The area of the sphere having a radius of 5 m is ...
A = 4πr² = 4π(5 m)² = 100π m² ≈ 314.16 m²
The sound intensity at that distance is ...
dB = 10·log(I/I0)
105 = 10·log(I/I0) . . . . substitute given values
10^10.5 = I/I0 . . . . divide by 10 and take the antilog
For such sound intensity measurements, the reference power level is ...
I0 = 10^-12 W/m²
Using this in the formula, we have ...
I = (10^10.5)·I0 = (10^10.5)·(10^-12 W/m²) = 10^-1.5 W/m²
Since the area of the sphere is 314.16 m², the total power of the siren is ...
(314.16 m²)(0.031623 W/m²) ≈ 9.93 W