At a rock concert, a dB meter registered 125 dB when placed 3.0 m in front of a
ID: 1264022 • Letter: A
Question
At a rock concert, a dB meter registered 125 dB when placed 3.0 m in front of a loudspeaker on the stage. (a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?W
(b) How far away would the sound level be a somewhat reasonable 92 dB?
m At a rock concert, a dB meter registered 125 dB when placed 3.0 m in front of a loudspeaker on the stage. (a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?
W
(b) How far away would the sound level be a somewhat reasonable 92 dB?
m (a) What was the power output of the speaker, assuming uniform spherical spreading of the sound and neglecting absorption in the air?
W
(b) How far away would the sound level be a somewhat reasonable 92 dB?
m
Explanation / Answer
a.
The expression for the intensity level of the sound wave is,
B = 10 dBlog[I/I0]
Rewerite the equation for the intensity of the sound wave.
I = I010(B/10) = 10-12*10(125/10) = 3.162 W/m2
The, the power output of the speaker is,
P = I [4*pi*r2] = 3.162*4*pi*32 = 357.6 W
b.
The intensity of the sound wave is,
I = I010(B/10) = 10-12*10(92/10) = 1.5848x10-3 W/m2
The required distance is,
r = [P/4*pi*I]1/2 = [357.6 / 4*pi*1.5848x10-3]1/2 = 134 m