Question

Two sources emit waves that are in phase with each other. What is the largest wavelength that will give constructive interference at an observation point 161 m from one source and 345 m from the other source?

Answer 1

Step-by-step explanation:

To determine the largest wavelength that will give constructive interference at the observation point, we can use the concept of path difference. Constructive interference occurs when the path difference between the two sources is an integer multiple of the wavelength.

Let's denote the distance from the first source to the observation point as d₁ = 161 m and the distance from the second source to the observation point as d₂ = 345 m.

The path difference (Δd) between the two sources can be calculated as:

Δd = d₂ - d₁

For constructive interference, the path difference must be an integer multiple of the wavelength (λ), so we can express this as:

Δd = n * λ

where n is an integer representing the number of complete wavelengths.

Substituting the values of d₁ and d₂, we have:

Δd = 345 m - 161 m

Δd = 184 m

Since Δd must be equal to n * λ, we need to find the largest possible wavelength (λ) that satisfies this condition. The largest possible value for λ occurs when n = 1 (minimum value for the path difference). Therefore:

184 m = 1 * λ

λ = 184 m

Thus, the largest wavelength that will give constructive interference at the observation point is 184 meters.