Phase difference and path difference

Two waves are in phase if they are both at the same point of the wave cycle, meaning they have the same frequency and wavelength (are coherent) and their phase difference is an integer multiple of 360° (2π radians). The waves do not need to have the same amplitude, only the same frequency and wavelength.

Two waves are completely out of phase when they have the same frequency and wavelength (are coherent) and their phase difference is an odd integer multiple of 180° (π radians).

The phase difference (in radians) of two waves with the same frequency and their path differences are related as shown below:

Where Δx is the path difference, λ is the wavelength of the waves and ΔΦ is their phase difference.

Below is an example question where you have to use the above relation. Two waves have a path difference of 6m and both have a wavelength of 2m, what is the phase difference of these two waves?

Firstly, rearrange the above relation so that the phase difference is the subject.

Then, substitute in the given values.

And so, their phase difference is 6π. As 6π is a multiple of 2π, the waves must be in phase.