How Far Can a Bird Watcher Hear a Song Bird's Sound?

[MarineBio]

Homework Statement

A bird watcher is hoping to add a particular song bird to the list of species she has seen. If a person, only 2.11 m from the bird, hears the sound with an intensity of 2.5 x 10^-6 W/m2, how far could the bird watcher be from the bird and still hear it? Assume no reflections or absorption of the bird's sound and that the faintest sound that can be heard has an intensity of 10^-12 W/m2.

Homework Equations

Speed of sound: 343 m/s

The Attempt at a Solution

Ok so I've determined that 2.5 x 10^-6 W/m^2 is 63.979 dB

and...

10^-12 W/m^2 is 10 dB

Now the problem is, I don't know if dB is even relevant to solving this equation, and what is worse: I don't even know what kind of equation to use in order to approach this problem :(

 

[Chi Meson]

dBs are not relevant here, and anyway 10^-12 W/m^2 is zero dB.

What you do need to know is that sound intensity has an inverse-square proportionality with distance.

If I move twice as far away, intensity will be the (inverse-square of 2) times the initial intensity (or 1/4 x). In other words, the ratio of initial intensity over final intensity will be equal to the ratio of final distance squared over initial distance squared.

 

[MarineBio]

Ok so Ii/If = (xf^2)/(xi^2)

so

(2.5x10^-6)/(10^-12) = (xf^2)/(2.11 m^2)

2,500,000 = (xf^2)/(2.11 m^2)

11,130,250 = xf^2

x = SRTQ(11,130,250)

x = 3336 m

x = 3.336 km

I think that looks about right, thank you very much!

 

[ideasrule]

Yes, that's the right answer.