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 P and distance to speaker is d.
1 2 3 4 5  Power of speaker is 2P and distance to speaker is 2d.
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 9P and distance to speaker is 3d.

Explanation / Answer

intensity=power/(4*pi*distance^2)

situatiion 1: intensity=power/(4*pi*distance^2)=0.25*P/(4*pi*(0.5*d)^2)=0.07957*P/d^2

situation 2:intensity=power/(4*pi*distance^2)=P/(4*pi*d^2)=0.07957*P/d^2

situation 3:intensity=power/(4*pi*distance^2)=2*P/(4*pi*(2*d)^2)=0.03978*P/d^2

situation 4: intensity=power/(4*pi*distance^2)=(1/9)*P/(4*pi*(3*d)^2)=9.8243*10^(-4)*P/d^2

situation 5:intensity=power/(4*pi*distance^2)=9*P/(4*pi*(3*d)^2)=0.25*P/d^2

hence situation 5> situation 1=situation 2> situation 3> situation 4

so ranking is as follows:

so situation 1:3

sitation 2: 3

situation 3: 2

situation 4:1

situation 5:5

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.