weather emergency siren is mounted on a tower, 141 meters above the ground. On o
ID: 1425169 • Letter: W
Question
weather emergency siren is mounted on a tower, 141 meters above the ground. On one hand, you would like to make the siren very loud so that it will warn as many people as possible. On the other hand, safety regulations prohibit you from exceeding an intensity level of 111 dB for workers standing on the ground directly below the siren. Assuming that the sound is uniformly emitted, what is the maximum power that the siren can put out? How far away from the base of the tower can a person be and still be able to hear the siren?Explanation / Answer
(i)
Assuming power levels are measured with respect to the standard threshold of hearing .. P = 1.0^-12 W/m²
Log P = -12
Let the power at the tower base = P .. .. dB = 10 log(P/P)
dB = 10(log P - log P)
Log P = dB/10 - 12 = 111/10 - 12 .. ..log P = -1.74 =P = 0.17 W/m²
The original power from the siren has now spread-out uniformly in all directions over a surface with a radius 141*10^-3km
from the siren .. spread over an area A = 4r² (surface area of a sphere)
Siren power .. Ps(W) = 0.17 W/m² x (4 x (141*10^-3)²)m² .. .. Ps = 0.0427k W
(ii) Assuming at the max distance (R) the power has reduced to the standard threshold value 1.0^-12 W/m²
Ps =0.0427 W = (1.0^-12 W/m²) x 4R²
R = {0.0427 / (1.0^-12 x 4)} .. .. R = 0.058 km
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