Abe and Bob are bird-watching, hoping to add a particular song bird to their \"l

Question

Abe and Bob are bird-watching, hoping to add a particular song bird to their "life list" of species. They agree to split up so they can cover a larger area. Abe hears the coveted bird's call with an intensity of 2.10 10-6 W/m2 when the bird is 2.03 m away from him.
(You may assume the bird call is of constant loudness, for simplicity's sake.)

a.) How loud (in dB) is the bird call to Abe?____dB
b.) Bob is as far away as possible, such that he can still hear the bird. How far away is he from the bird? ____km
c.) A typical surface area of an eardrum is 5

Explanation / Answer

(a) sound level = 10 log(2.10x10^-6 / 1x10^-12) = 63.22 dB

(b) intensity for Abe / intensity for Bob = (distance for bob / distance for Abe)^2

2.10x10^-6 / 1x10^-12 = (d / 2.03)^2

d = 2942 meters = 2.942 km

(c) energy = intensity * area * time * two ears

Abe: energy = 2.10x10^-6 * 5x10^-5 * 4 * 2 = 8.40 x 10^-10 Joules

Bob: energy = abe's energy * (abe distance / bob distance)^2 =

= 8.40x10^-10 * (2.03 / 2942)^2 = 4.00 x 10^-16 Joules

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