Find Sound Power of Motor Car - 0.354 W

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SUMMARY

The sound power of a motor car, calculated based on a sound level of 87 dB at a distance of 7.5 meters, is determined to be 0.354 W. This calculation uses the formula for sound intensity, I = P / (4πr²), where I is the intensity and r is the distance from the source. The discrepancy with the teacher's answer of 0.18 W arises from the assumption of sound energy distribution; the sound reflects off the ground, affecting the effective area over which the sound power is spread.

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Hello! I am doing some questions about sound waves for my homework assignment and have some problem in one of them.
Assuming that it radiates sound uniformly, find the sound power from a motor car whose sound level at a distance of 7.5m is 87dB.
Here are my steps:
I = sound intensity, I_0 = minimum audible intensity
By h = 10log(I/I_0)
87 = 10 log (I / 10x10^-12)
I = 5.01 x 10^-4 W/m^2
By I = P / 4 pi r^2
5.01x 10^-4 = P / 4 pi 7.5^2
P = 0.354W
But the answer given by my teacher is 0.18W...Can anyone tell me what's wrong in my calculation.:smile: Thanks!
 
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I also got P = 0.354W.
 
You were having the Sound Energy travel downward, into the ground.
Almost all the sound will reflect from the solid Earth -
spreading over the upper (air) hemisphere, 2 pi r^2 .
 

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