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A spherical source radiates sound uniformly in all directions
A spherical source radiates sound uniformly in all directions. At a distance of 19 m, the sound intensity level is 120 dB.
(a) At what distance from the source is the intensity level 40 dB?
m
(b) What power is radiated by this source?
W
Expert Solution
Answer:
We know that, P = I A = I (4 pi r2)
(a) At what distance from the source is the intensity level 40 dB?
I1 A1 = I2 A2
(120 dB) 4 (pi) (19 m)2 = (40 dB) 4 (pi) x2
(43320 W) = (40 dB) x2
x2 = (1083 m2)
x = 32.9 m
(b) Power radiated by this source which will be given as :
using a formula, we have
SIL (dB) = 10 log10 (I / I0)
(120) / (10) = log10 [I / (10-12 W/m2)]
(12) = log10 [I / (10-12 W/m2)]
I / (10-12 W/m2) = 1012
I = 1 W/m2
We know that, P = I A = (1 W/m2) 4 (3.14) (19 m)2
P = 4534.1 W
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