Answer:
Suppose that the wave equation is:
f(x) = A*cos(k*x)
The wave is in phase for two points x₁ and x₂ if:
f(x₁) = f(x₂)
And if these points are consecutive (for example, two consecutive peaks) then the wavelength of the wave is:
wavelength = x₂ - x₁
In this case, we know that the wave is in phase for two points that are 2 m apart.
Then we can use the points:
x₁ and x₂ such that:
x₂ = x₁ + 2m
We also know that these are the nearest points such that this happens, then we can assume that the points are consecutive.
Then the wavelength will be:
wavelength = x₂ - x₁ = (x₁ + 2m) - (x₁) = 2m
Then the wavelength is 2m.
The correct option is C.
