Question

5.00 m from a siren, the sound

level is 105 dB. What is the power
of the siren?
(Treat the siren as a point source.)

Answer 1

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