Sound Intensity and Bird Watching

[majormaaz]

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 2.35 m from the bird, hears the sound with an intensity of 1.9 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

I2/I1 = (r1/r2)^2
I1 = 1.9e-6 W/m2
I2 = 10e-12 W/m2
r1 = 2.35 m
r2 = ?

The Attempt at a Solution

I rearranged the equation to solve for r2
I got r2 = √(I1 * r1^2/I2)
I plugged in the numbers and got 1024.34 meters
but the problem is saying that I did it wrong.
Is there another formula or did I just mess up somewhere in solving this?
Would appreciate help before Monday.
Thanks

 

[emailanmol]

Hey,

See Intensity is inversely proportional to square of distance which is exactly what you used.

So your equations are correct.

Plug in the values again :-)

 

[majormaaz]

Hey,

See Intensity is inversely proportional to square of distance which is exactly what you used.

So your equations are correct.

Plug in the values again :-)

Thanks for the reassurance. However, I found out that my value for the Intensity of the threshold of hearing was wrong by a power. Thanks though

 

[emailanmol]

Oh.Lol.!

Yeah using 10^(-11) W/m^2 yields exactly the answer in your Post 1.

 

[asteriatic]

I would approach this problem by first considering the concept of sound intensity and how it relates to distance. Sound intensity is a measure of the amount of sound energy passing through a given area in a certain amount of time. It follows the inverse square law, meaning that as distance from the source increases, the sound intensity decreases proportionally. This means that the further away the bird watcher is from the bird, the lower the sound intensity will be.

Next, I would use the given information to calculate the sound intensity at the bird watcher's distance. Using the equation I = P/A, where I is sound intensity, P is sound power, and A is the area through which the sound is passing, we can solve for P. In this case, P is the sound power of the bird's song, which we do not know. However, we can use the given information about the faintest sound that can be heard (10-12 W/m2) to approximate the bird's sound power. This leads to the equation P = I * A.

We know the sound intensity at the bird watcher's distance (1.9 * 10-6 W/m2) and the area through which the sound is passing (4πr2, where r is the distance from the bird). Plugging in these values, we get P = (1.9 * 10-6 W/m2) * (4πr2). Solving for r, we get r = √(P/(1.9 * 10-6 W/m2 * 4π)).

We can now use the given information about the faintest sound that can be heard to solve for the distance at which the bird watcher can still hear the bird's song. Plugging in the sound power we approximated earlier (10-12 W/m2), we get r = √((10-12 W/m2)/(1.9 * 10-6 W/m2 * 4π)) = 1.15 meters.

This means that the bird watcher could be up to 1.15 meters away from the bird and still hear its song. It is important to note that this is a rough approximation and there may be other factors at play that could affect the sound intensity and the distance at which the bird can be heard. However, based on the given information, this is a reasonable estimate.