Question

A bird-watcher is hoping to add a particular song bird to her "life list" of species. If a person, only 1.93 m from the bird, hears the sound with an intensity of 2.40 10-6W/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. 1.55 e-3 Incorrect: Your answer is incorrect. km

Answer 1

We know that the
Power = Intensity*area
Power = Intensity*(4r²)
where r is the distance from the bird
Now since the power will remain constant therefore
I₁A₁ = I₂A₂
I₁*(4r₁²) = I₂*(4r₂²)
where r₁ is the distance initially
I₁ = 2.40 10^-6 w/m² is the intensity when the distance is r₁
I₂ = 10^-12 w/m² when the distance is r₂
Now applying the value in above equation
2.40 10^-6*(4r₁²) = 10^-12 *(4r₂²)
2.40 10^-6*(4*1.93²) = 10^-12 *(4r₂²)
r₂ = 2.989*10³ m
r₂ = 2.989 km