Simple sound intensity difficulty

[Vanessa23]

According to the text, at a distance of 50 m from a jet engine, the sound intensity is 10 W/m2. This corresponds to a loudness (or an intensity level) of 130 dB. [You should convince yourself that this is true.] If you find the sound too loud and you want to reduce the intensity by a factor of 10, to what new distance (approximately) from the jet engine should you move to achieve this reduction?


I=P/Area

Intensity level = 10db*log(I/Io)


to find the power of the jet engine:
p=10*((50^2)*4pi)
=314159

a factor of 10 reduction would mean 13dB
13=10log(I/10^-12)
1.3=log(I)-log(10^-12)
-10.7=log(I)
I=10^-10.7

A=P/I
A= 314159/ 10^-10.7
A=1.57x10^16

1.57x10^16 = 4pi r^2
r=397289

so does that mean that you really can't make the intensity decrease by a factor of 10?

 

[catkin]

I don't think dB need to come into the calculation; the question asks for a reduction in intensity, not in "intensity level" or loudness.

The requisite new level is a factor of 10 less than the first level of 10 W/m^-2, that is 1 W/m^-2.

Assuming the jet engine is on a plane surface and there are no reflections then the noise power is radiating through the surface of a hemisphere ...

 

[ogb p]

Based on the calculations, it appears that the distance from the jet engine would need to be approximately 397289 meters in order to achieve a reduction in intensity by a factor of 10. However, this distance may not be practical or even possible in real-world scenarios. Other methods, such as using sound-absorbing materials or ear protection, may be more effective in reducing the perceived loudness of the jet engine. Additionally, it is important to note that sound intensity and loudness are subjective and can vary depending on individual perception and other factors such as frequency and duration of exposure. As a scientist, it is important to consider all variables and potential limitations when interpreting and applying scientific principles.