Question

An audio speaker at a concert emits sound uniformly in all directions at a rate
of 100 W.
(i) Calculate the sound intensity experienced by a listener at a distance
of 8 m from the speaker.
The listener moves back from the speaker to protect her hearing.
(ii) At what distance
from the speaker is the sound intensity level reduced by 3 dB?

Answer 1

I = P/A = P/4πr² = 100/4π(8)² = 0.12 W•m⁻²
If the sound intensity level is halved to a value of I = 0.06 W•m⁻²,
the sound intensity level will decrease by 3 dB.
I = P/4πr² = 100/4π(x) ² =
=0.06 W•m⁻²
x = 11.5 m from the speaker.

Answer 2

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