What is the 'path difference' in waves

[Ichijou Maeve]

My textbook states that:

"Points P₁ and P₂ are both on antinodal lines. The length of the path traveled by wave 1 from its source (S₁) to point P₁ is two wavelengths. The length of the path traveled by wave 2 from its source (S₂) to point P₁ is three wavelengths. The path difference (pd) is therefore one wavelength; pd = 1 λ. All points on the antinodal line n = 1 have the path difference pd = 1 λ."

But no matter how many times I read through it I just don't understand what a path difference is meant to be... Could I get a clear explanation of what a path difference is and why it is important?

Thank you,

Ichijou

 

[Born2bwire]

In this case, it's simply the difference in the distance traveled by the wave going from the source one to point one versus source two to point two. They have decided to express it in terms of wavelength.

The path difference is important because the phase of a wave has a spatial dependence. If we generate a wave at some point and observe it after it has traveled 1 m and then 2 m, the phase of the wave at these points may be different. The only exception would be if the two points differ by an integral multiple of the wavelength (in which case the phase shift is a multiple of two \pi and the phase is the same). If we have two different sources, then the behavior of the total field from the two individual waves will depend upon the relative phase. At some points we may see strong deconstructive interference and others strong constructive interference. It all depends upon the phase difference between the two waves at a given point. This phase dependence depends upon the phase of the wave at the source and the distance the waves traveled to the observation point.