Final answer:
The distance from source A where there is constructive interference between points A and B is 4.0 meters.
Step-by-step explanation:
To determine the distance from source A where there is constructive interference between points A and B, we need to consider the path difference between the two waves. Constructive interference occurs when the path difference is an integer multiple of the wavelength. In this case, the wavelength is given as 6.00 meters.
Since the two sources are 5.00 meters apart, the path difference between points A and B is equal to the distance from source A to the point of constructive interference minus the distance from source B to the same point. Let's call the distance from source A to the point of constructive interference x meters.
Therefore, the path difference is 2(x - 5.00) = 2x - 10.00 meters. This path difference must equal an integer multiple of the wavelength 6.00 meters. So, 2x - 10.00 = 6.00n, where n is an integer.
Simplifying the equation, we have 2x = 6.00n + 10.00. Dividing both sides by 2, we get x = 3.00n + 5.00. This equation shows that the distance from source A to the point of constructive interference can be expressed as a multiple of 3.00 meters plus 5.00 meters.
So, by substituting different values of n (integer values) into the equation, we can find the distance from source A where there is constructive interference.
For n = 0, x = 3.00 × 0 + 5.00 = 5.00 meters. This corresponds to the distance between source A and point A. Constructive interference occurs at point A.
For n = 1, x = 3.00 × 1 + 5.00 = 8.00 meters. So, at a distance of 8.00 meters from source A, there is constructive interference between points A and B.
Therefore, the correct answer is 4.0 meters.