A siren at the top of a tall building emits sound isotropically (uniformly in al
ID: 1602207 • Letter: A
Question
A siren at the top of a tall building emits sound isotropically (uniformly in all directions.) When you are a short distance from the base of the building, your measuring device on the ground indicates the intensity level 98.4 dB. You then move 90.0 m further away from the base of the building and find the intensity level (at the ground) is 92.0 dB. If the height of the building is 20.0 m, find the power emitted by the siren.
Note: The answer is suppose to be 576W but I keep on getting something much smaller in wattages.
Explanation / Answer
here,
let the power emmited by the siren be P and the distance from the base of building be x
height of the building, h = 20 m
I = inv log {(dB/10) - 12}
P /( pi*(x^2 + h^2)) = invlog((98.4/10) - 12)
P /( pi*(x^2 + 20^2)) = invlog((98.4/10) - 12) .....(1)
when he moves 90 m further,
P /( pi*((x + 90 )^2 + 20^2)) = invlog((92/10) - 12) .....(2)
from equation (1) and (2)
P = 576.26 W and x = 78.92 m
The power of the source is 576.26 W (Ans)