A listener hears a sound emitted isotropically by a loudspeaker (L1) located 10

Question

A listener hears a sound emitted isotropically by a loudspeaker (L1) located 10 m away. The sound is emitted
with a power P1 = 250 W.
a (5pts) - what is the intensity of the sound from loudspeaker L1 at the listener’s position?
The listener then decides to switch off loudspeaker (L1) and try another loudspeaker (L2) located also 10 m
away from the listener. Loudspeaker (L2) has a power P2 = 300 W.
b - what is the intensity of the sound from loudspeaker L2 at the listener’s position?
c - What is the difference in sound level (in dB) between sounds from loudspeaker L2 and loudspeaker
L1?

Explanation / Answer

Given data : P1 = 250 W         ; P2 = 300 W

                   r1 = 10 m           ; r2 = 10 m

a) I1 = P1/A = 250/(4r12) = 0.199 W/m2

b) I2 = P2/A = 300/(4r22) = 0.239 W/m2

c) 2 = 10 log I2/Io = 10 log [0.239/10-12] = 113.784 dB             with Io = 10-12 W/m2

    1 = 10 log I1/Io = 10 log [0.199/10-12] = 112.988 dB

= 2 -1 = 0.796 dB

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