26. Two small speakers emit sound waves of differentfrequencies equally in all d

Question

26. Two small speakers emit sound waves of differentfrequencies equally in all directions. Speaker A has an output of 1mW, and speaker B has an output of 1.5mW. Determine the sound level(in decibels) at point C which is a perpindicular distance of 4maway from the two speakers facing each other horizontally.The twospeakers are 5m apart, The sound waves emitted from speaker A carry3m toward speaker B and the sound waves emitted from speaker Bcarry 2m toward Speaker A. Point C is 4m directly perpindicular towhere the waves of speaker A and B meet. a) only speaker A emits sound b) only speaker B emits sound c) both speakers emit sound Thanks for your help. I will rate well. 26. Two small speakers emit sound waves of differentfrequencies equally in all directions. Speaker A has an output of 1mW, and speaker B has an output of 1.5mW. Determine the sound level(in decibels) at point C which is a perpindicular distance of 4maway from the two speakers facing each other horizontally.The twospeakers are 5m apart, The sound waves emitted from speaker A carry3m toward speaker B and the sound waves emitted from speaker Bcarry 2m toward Speaker A. Point C is 4m directly perpindicular towhere the waves of speaker A and B meet. a) only speaker A emits sound b) only speaker B emits sound c) both speakers emit sound Thanks for your help. I will rate well.

Explanation / Answer

This requires several steps: --   find the distance from each speaker to pointC --   find the intensity at point C from eachspeaker --   find the sound level from the intensity . So... .       distance from A to C = (32 + 42)1/2 =    5 m .     distance from B to C = (22 + 42)1/2   =  20 m .     intensity from speaker A = power / 4r2 = 0.001 / 4*25 =    3.18309 x 10-6 W/m2 .    intensity from speaker B = power /4r2 = 0.0015 / 4*20 =    5.9683 x 10-6 W/m2 .     intensity of both = 3.18309 + 5.9683   =   9.1514 x10-6 W/m2 . finally... .      sound level for speaker A alone = 10 log (I / I0 ) = 10 log(3.18309 x10-6 / 1 x 10-12) = .                 =     65.03 dB .      sound level for speaker B alone = 10 log(5.9683 x 10-6 / 1 x10-12) = 67.76 dB .       sound level for bothtogether = 10 log(9.1514 x 10-6 / 1 x10-12) =    69.61 dB . finally... .      sound level for speaker A alone = 10 log (I / I0 ) = 10 log(3.18309 x10-6 / 1 x 10-12) = .                 =     65.03 dB .      sound level for speaker B alone = 10 log(5.9683 x 10-6 / 1 x10-12) = 67.76 dB .       sound level for bothtogether = 10 log(9.1514 x 10-6 / 1 x10-12) =    69.61 dB

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