Question

The sound intensity 50m from a wailing tornado siren is 0.1W/m2 . What is the sound intensity level 300m from the siren?

Answer 1

Answer:

$I_{300} =2777.7uW/m^{2}$

Explanation:

Looking at the formula of intensity we can see that it is inversely proportional to the square of distance and the other terms are all constant

So

$I=\frac{P}{A}\\I=\frac{P}{\pi d^{2} }\\I=C\frac{1}{d^{2} }$

We can now write the following equality

$\frac{I_{300} }{I_{50}}=\frac{50^{2} }{300^{2} }\\ I_{300} =\frac{50^{2} }{300^{2} }*I_{50}\\I_{300} =0.02777*I_{50}$

Substitute the know intensity at 50m we get

$I_{300} =0.02777(0.1W/m^{2} )\\I_{300} =2777.7uW/m^{2}$