A bird-watcher is hoping to add the white-throated sparrow to her "life list" of species. How far could she be from the bird described in example 14-8 and still be able to hear it? Assume no reflections or absorption of the sparrow's sound.

Answer:5290m or 5.3km

Explanation:

The sound swirls out according to law of inverse square.

Which means the intensity is inversely proportional to square of the distance:

That is

I ∝ 1/d²

this is then,

I = k/d²

Given that

d=1.00m, I = 2.80*10⁻⁵ W/m².

We have

k = Id² = 2.80*10⁻⁵ x 1.00² = 2.80*10⁻⁵ W

(But k = power output of the bird.)

Human hearing limit is usally taken as an intensity of 10⁻¹² W/m². The distance that gives this intensity is calculated as follows:

I = k/d²

10⁻¹² = 2.80*10⁻⁵ / d²

d² = 2.80x10⁷

d = 5290m (to 3 sf)

=5.3km