Final answer:
The intensity at a distance of 4.00 m from the source is 1/16th of the initial intensity. The distance from the tuning fork where the intensity is a tenth of the intensity at the source is approximately 3.16 meters.
Step-by-step explanation:
(a) To find the intensity at a distance of 4.00 m from the source, we can use the inverse square law, which states that the intensity is inversely proportional to the square of the distance.
In this case, the initial intensity at one meter from the source is given as I₁. So, we can use the following formula:
Intensity₂ = Intensity₁ * (Distance₁/Distance₂)²
Plugging in the values, we have:
Intensity₂ = I₁ * (1/4)² = I₁/16
Therefore, the intensity at a distance of 4.00 m from the source is 1/16th of the initial intensity (I₁/16).
(b) To find the distance from the tuning fork where the intensity is a tenth of the intensity at the source, we can use the inverse square law again. We can set up the following equation:
I₁ * (1/x)² = (1/10) * I₁
Simplifying, we get:
(1/x)² = 1/10
Taking the square root of both sides, we find:
1/x = 1/√10
Therefore, the distance from the tuning fork where the intensity is a tenth of the intensity at the source is approximately 3.16 meters.