Suppose a speaker is sending out a signal of a given power uniformly in all dire

Question

Suppose a speaker is sending out a signal of a given power uniformly in all directions. You are located a certain distance from the speaker measuring the intensity of the sound. Given the following different situations, rank the measured intensity (1 = the lowest intensity).
1 2 3 4 5  Power of speaker is (1/4)P and distance to speaker is (1/2)d.
1 2 3 4 5  Power of speaker is 3P and distance to speaker is 3d.
1 2 3 4 5  Power of speaker is P and distance to speaker is d.
1 2 3 4 5  Power of speaker is 9P and distance to speaker is 3d.
1 2 3 4 5  Power of speaker is 9P and distance to speaker is (1/3)d.

Explanation / Answer

The sound intensity decreases with distance to source. Intensity and distance can be expressed as
I = Pi / 4**r^2

Now you just insert values, to calculate I

(1)

(1/4) p and distance to speaker is (1/2)d.
Pi = (1/4)P

r=1/2d
I = (1/4)P/(4*pi*(0.5d)^2)

= 0.25*P/(pi*d^2) W/m^2

(2)

Power of speaker is 3P and distance to speaker is 3d.

Pi = 3P

r = 3d
I = 3P/(4*pi*(5d)^2)

= 0.0833 *P/(pi*d^2) W/m^2

(3)

Power of speaker is P and distance to speaker is d.
Pi = P

r = d
I = P/(4*pi*(d)^2)

= 0.25 P/(pi*d^2) W/ m^2

(4)

Power of speaker is 9P and distance to speaker is 3d.
Pi = 9P

r = 3d
I = 9P/(4*pi*3d^2)

= 0. 25*Pi/(pi*d^2) W/m^2

(5)

Power of speaker is 9P and distance to speaker is (1/3)d.
Pi = 9P

r = (1/3)d
I = 9P/(4*pi*(1/3*d)^2)

= 20.29*P/(pi*d^2) W/m^2

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