A. Suppose a speaker is sending out a signal of a given power uniformly in all d

Question

A. 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 4P and distance to speaker is (1/2)d.
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.

B. You are standing in the middle of a large room listening to a cacaphony of sounds. Rank the intensity of the sounds from each source (1=loudest, 2= next loudest, ...) Consider all objects to be right next to you. If two values are within 0.1 dB from each other, consider them to be the same.
1 2 3 4  An object emitting a sound with an intensity level of 80dB.
1 2 3 4  Two buzzers each producing a sound with intensity level of 70 dB.
1 2 3 4  An object emitting a sound with an intensity of 1.0×10-5 W/m2.
1 2 3 4  An object emitting a sound with an intensity level of 90 dB.

C. You are standing in the middle of a large room listening to a cacaphony of sounds. Rank the intensity of the sounds from each source (1=loudest, 2= next loudest, ...) Consider all objects to be right next to you. If two values are within 0.1 dB from each other, consider them to be the same.
1 2 3 4 5  An object emitting a sound with an intensity of 1.0×10-9 W/m2.
1 2 3 4 5  100 buzzers each producing a sound with intensity level of 60 dB.
1 2 3 4 5  An object emitting a sound with an intensity level of 20dB.
1 2 3 4 5  Two buzzers each producing a sound with intensity level of 70 dB.
1 2 3 4 5  An object emitting a sound with an intensity level of 90 dB.

D. You are standing in the middle of a large room listening to a cacaphony of sounds. Rank the intensity level of the sounds from each source (1=loudest, 2= next loudest, ...) Consider all objects to be right next to you. If two values are within 0.1 dB from each other, consider them to be the same.
1 2 3 4 5  Two buzzers each producing a sound with intensity level of 57dB.
1 2 3 4 5  Ten buzzers each producing a sound with intensity level of 50dB.
1 2 3 4 5  An object emitting a sound with an intensity level of 60dB.
1 2 3 4 5  One hundred buzzers each producing a sound with intensity level of 40dB.
1 2 3 4 5  Four buzzers each producing a sound with intensity level of 54dB.

E. You are standing in the middle of a large room listening to a cacaphony of sounds. Rank the intensity level of the sounds from each source (1=loudest, 2= next loudest, ...) Consider all objects to be right next to you. (Remember that if you have a tie, you skip some ranks.) If two values are within 0.1 dB from each other, consider them to be the same.
1 2 3 4  Ten buzzers each producing a sound with intensity level of 82dB.
1 2 3 4  Two buzzers each producing a sound with intensity level of 86dB.
1 2 3 4  Four buzzers each producing a sound with intensity level of 81dB.
1 2 3 4  An object emitting a sound with an intensity of 90dB.

Explanation / Answer

A] The intensity measured will be directly proportional to the power and inversely proportional to square of the distance.

Since I = Power/Area

so, for 9P and 3d, the intensity will be proportional to 9P/(3d)2 = P/d

for 4P and (1/2)d, the intensity will be proportional to 4P/(0.5d)2 = 16P/d [LARGEST]

for (1/4)P and (1/2)d, the intensity will be proportional to (1/4)P/(0.5d)2 = P/d

for 3P and 3d, the intensity will be proportional to 3P/(3d)2 = (1/3)P/d [SMALLEST].

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