Question

Two small loudspeakers emit sound waves of different frequencies equally in all directions. Speaker A has an output of 1.30 mW, and speaker B has an output of 1.90 mW. Two speakers A and B are represented as points which serve as the centers of concentric circles representing sound waves emanating from the speakers. The concentric circles about speaker A are spaced more closely together than the concentric circles about speaker B. The points lie along a horizontal line, and speaker A is 5.00 m to the left of speaker B. A vertical line is drawn that intersects the horizontal line at a distance of 3.00 m from the left speaker and 2.00 m from the right speaker. Point C lies along this vertical line at a distance of 4.00 m above the point of intersection. (a) Determine the sound level (in decibels) at point C in the figure if only speaker A emits sound. (Enter your answer to at least one decimal place.) dB (b) Determine the sound level (in decibels) at point C in the figure if only speaker B emits sound. (Enter your answer to at least one decimal place.) dB (c) Determine the sound level (in decibels) at point C in the figure if both speakers emit sound. (Enter your answer to at least the nearest dB.) dB/Users/crystaldawnmcclendon/Desktop/14-p-064.gif

Answer 1

a) From the figure we can assume that the speaker A is 3 m from the horizontal line of speaker C

From the figure we can assume that the speaker B is 2 m from the horizontal line of speaker C

and the intensity of the sound from this speaker is

The sound level at C due to speaker A alone is then

(b) The distance from point C to speaker B is

and the intensity of the sound from this speaker alone is

The sound level at C due to speaker B alone is therefore

(c) If both speakers are sounded together, the total sound intensity at point C is

I_AB = I_A + I_B = 4.13X10^-6 W/m² + 7.56 x10^-6 W/m² = 11.69 x 10 ^-6 W/m²

and the total sound level in decibels is