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 9P 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 (1/9)P and distance to speaker is 3d.
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 2P and distance to speaker is 2d.

Explanation / Answer

Here we have to intensity and distance .....relation b/w them is :

I = Pi/4**r^2 ===================================eq (1)

here Pi is represented as power

r= radius

1) We have Pi = 9p and r=3d

put them in the above equation

I = 9 P/(4*pi*(3d)^2) = = = = = 0.25 *P/(pi*d^2) W/m^2 ----------------------------

2)  Pi=P r=d
I=0.25 *P/(pi*d^2) W/m^2 ------------------------------

3) P/(9*9)d^2 = 0.003086 P/(pi*d^2) W/m^2  -------------------------

4) I=0.25P/(4*pi*(0.5d)^2)=0.25 *P/(pi*d^2) W/m^2---------------

5) 2P/4d^2 = 0.125P/(pi*d^2) W/m^2 ---------------

so the final order is :

3) < 5) = 4) = 2) =1) -------------------------i have taken order according to the numbering I have mentioned....you can change accordingly if you need.

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