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

`I_(300) =2777.7uW/m^(2)`

Step-by-step 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=(P)/(A)\\I=(P)/(\pi d^(2) )\\I=C(1)/(d^(2) )`

We can now write the following equality

`(I_(300) )/(I_(50))=(50^(2) )/(300^(2) )\\ I_(300) =(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)`