A spherical source radiates sound uniformly in all directions. At a distance of 12 m, the sound intensity level is 100 dB. At what distance from the source is the intensity level 40 dB?
When I set it up as 100dB/40dB = r^2/(12m)^2, and got x = 18.97 meters, i was told this answer was incorrect.
To solve this problem, we need to use the inverse square law for sound intensity, as the sound is radiating uniformly in all directions from a spherical source.
The inverse square law states that the sound intensity decreases with the square of the distance from the source. Mathematically, it can be expressed as:
I₁ / I₂ = (r₂ / r₁)²
Where I₁ and I₂ are the sound intensities at distances r₁ and r₂ respectively.
In this case, we have I₁ = 100 dB and r₁ = 12 m. We want to find r₂ when I₂ = 40 dB.
Let's plug the values into the equation:
100 dB / 40 dB = (r₂ / 12 m)²
Using this equation, let's solve for r₂:
(100 / 40) = (r₂ / 12)²
Simplifying, we get:
2.5 = (r₂ / 12)²
Taking the square root of both sides, we get:
√2.5 = r₂ / 12
r₂ = 12 * √2.5
Evaluating this expression, we find:
r₂ ≈ 18.97 m
So, the correct answer should indeed be approximately 18.97 meters. It seems that your answer is correct, and there might have been an error in the feedback you received.