Two small speakers emit sound waves of different frequencies

Two small speakers emit sound waves of different frequencies equally in all directions. Speaker A has an output of 0.500 mW, and speaker B has an output of 2.00 mW.

(a) Determine the sound level (in decibels) at point C assuming only speaker A emits sound. dB

(b) Determine the sound level (in decibels) at point C assuming only speaker B emits sound. dB

(c) Determine the sound level (in decibels) at point C assuming both speakers emit sound. dB

Solution

AC = sqrt [3² + 4²] = 5 m

I = P / 4 pi AC² = 0.0005 / 4 pi * 25 = 1.59 * 10^-6 W/m²

The sound level at point C

10 log I/I₀ = 10 log (1.59 * 10^-6 / 10^-12) = 62.0 dB

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BC = sqrt [2² + 4²] = 4.47 m

I = P / 4 pi AC² = 0.002 / 4 pi * 4.47² = 7.97 * 10^-6 W/m²

The sound level at point C

10 log I/I₀ = 10 log (7.97 * 10^-6 / 10^-12) = 69.0 dB

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Itotal = (1.59 * 10^-6 ) + (7.97 * 10^-6) = 9.56 * 10^-6 W/m²

10 log I/I₀ = 10 log (9.56 * 10^-6/ 10^-12) = 69.8 dB