Find Sound Power of Motor Car - 0.354 W

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The discussion revolves around calculating the sound power of a motor car based on its sound level measured at a distance of 7.5 meters. The initial calculation yielded a sound power of 0.354 W using the formula for sound intensity and the relationship between intensity and power. However, the teacher's answer of 0.18 W suggests a discrepancy. A participant pointed out that sound energy primarily travels upward, with most sound reflecting off the ground, which may affect the calculations. The conversation highlights the importance of considering sound propagation in different environments when determining sound power.
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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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