How Far Must You Be from a Tornado Siren for a 15 dB Decrease in Sound?

[Jayhawk1]

Here is the trouble problem...

11) A tornado warning siren on top of a tall pole radiates sound waves uniformly in all directions. At a distance of 15 m the sound intensity of the siren is 0.39 . Neglect any effects from reflection of the sound waves from the ground. a) At what distance from the siren is the intensity 0.19 ? b) What is the total acoustical power output of the siren? c) At what distance is the sound intensity reduced by 15 dB from its level at 15 m?

a) 21.5 m
b) 1100 Watts

Ok... so I figured out parts a and c, but I have no clue for part c- and the same seems to go for most of my class. I think the change might be very small, but I don't know how to get it. Any help would be appreciated. Thanks!

 

[OlderDan]

What are the dimensions of .39 and .19? Knowing that should lead you to an answer for b) I believe the customary dimensions would give you intensity in watts/meter^2. Intensity is the power per unit area, and the area in your case is the total area of the sphere centered at the source.

 

[Jayhawk1]

Sorry... I meant I didn't understand part C... any help?

 

[OlderDan]

The decibel scale is based on logarithms. In terms of intensity

$$L = 10log({\frac{I}{I_0}})$$

You need to find the intensity ratio that gives you L = -15 and from that determine the distance ratio and then the final distance