Two loudspeakers on elevated platforms are at opposite ends of a field. Each bro

Question

Two loudspeakers on elevated platforms are at opposite ends of a field. Each broadcasts equally in all directions with the same power. The sound intensity level at a point halfway between the loudspeakers is 80.0 dB. Assume there are no interference effects for this problem. If the observer moves to a point that is one-quarter of the way from one speaker to the other along a line joining them, what is the intensity from the closer speaker If the observer moves to a point that is one-quarter of the way from one speaker to the other along a line joining them, what is the intensity from the farther speaker What is the sound intensity level at the new position beta_2 = 83.5 dB

Explanation / Answer

the intensity produced by each speaker at the point halfway between them is the same. Hence:
Itotal = I + I = 2I

L = 10log( 2I/I) with I= 10¹²W/m²

=> I = (10¹²W/m²) 10^(L/10)

=> I = 10-4 W/m2

=> intensity from one speaker = 0.5*10-4 W/m2

(a) intensity from close speaker = 4*0.5*10-4 W/m2

                                                    = 2*10-4 W/m2

(b) intensity from farther speaker = (4/9) * 0.5*10-4 W/m2

                                                                          = 0.222 *10-4 W/m2

(c) sound intensity at new position = 10log(20/9) + L

                                                        = 3.5 + 80

                                                         = 83.5 dB

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