MATH SOLVE

3 months ago

Q:
# 5.00 m from a siren, the soundlevel is 105 dB. What is the powerof the siren?(Treat the siren as a point source.)

Accepted Solution

A:

Answer: about 9.93 WStep-by-step explanation:The area of the sphere having a radius of 5 m is ... A = 4πr² = 4π(5 m)² = 100π m² ≈ 314.16 m²The 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 antilogFor such sound intensity measurements, the reference power level is ... I0 = 10^-12 W/m²Using this in the formula, we have ... I = (10^10.5)·I0 = (10^10.5)·(10^-12 W/m²) = 10^-1.5 W/m²Since 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