Aman stands at the midpoint between two speakers that are broadcasting an amplified static hiss uniformly in all directions. the speakers are 27.3 m apart and the total power of the sound coming from each speaker is 0.535 w. (answers in w/m^2). (a) find the total sound intensity that the man hears when he is at his initial position halfway between the speakers.
(b) find the total sound intensity that the man hears after he has walked 4.5 m directly toward one of the speakers.

Explanation:

The power of each of the speakers is 0.535 W. At a distance d intensity of sound can be found by the following formula

Intensity of sound =  Power / 4π d²

= .535 / 4 x 3.14 x (27.3/2)²

= 2.286 x 10⁻⁴ J m⁻² s⁻¹

Intensity of sound due to other source = 5.715 x 10⁻⁵J m⁻² s⁻¹

Total intensity = 2 x 2.286 x 10⁻⁴J m⁻² s⁻¹

= 4.57 x 10⁻⁴J m⁻² s⁻¹

b ) In this case, man is standing at distances 18.15 m and 9.15 m from the sources .

The total intensity of sound reaching him is as follows

0.535 / (4 π x18.15² ) + 0.535 /  (4 π x9.15² )

= 1.293 x 10⁻⁴ + 5.087 x 10⁻⁴

= 6.38 x 10⁻⁴J m⁻² s⁻¹

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