What is meant by 'path difference' in wave interference?

The concept of 'path difference' in wave interference refers to the difference in distances that two waves travel to reach a specific point. When two waves meet at a point in space, the length of the pathway that each wave has taken from its source to that point may vary. This difference in distance results in a path difference, which can determine how the waves interact with each other — either constructively or destructively.

In constructive interference, waves that arrive in phase (meaning their path difference is an integer multiple of the wavelength) amplify each other, leading to increased amplitude at that point. Conversely, in destructive interference, waves that arrive out of phase (where the path difference is a half-integer multiple of the wavelength) can cancel each other out, resulting in reduced or zero amplitude.

This concept is crucial for understanding phenomena such as patterns created in double-slit experiments or other wave interference scenarios. The relationship between path difference and the resulting wave interaction is foundational in wave theory. Thus, recognizing that the path difference specifically refers to the spatial distance traveled by each wave is key to analyzing and predicting wave behavior at various points in a medium.