What is meant by a wave's path difference?

A wave's path difference refers to the difference in distance travelled by two waves from their sources to a particular point.

In more detail, when two or more waves of the same frequency and type (for instance, sound waves or light waves) originate from different sources, they travel different distances to reach a common point. This difference in the distances they travel is known as the path difference. It is a crucial concept in wave interference and can determine whether the waves will constructively or destructively interfere at that point.

For instance, if two waves meet at a point and the path difference is a whole number multiple of the wavelength, they will constructively interfere, leading to a wave of greater amplitude. This is because the peaks (or troughs) of the waves align, causing them to add together. On the other hand, if the path difference is an odd multiple of half the wavelength, the waves will destructively interfere, resulting in a wave of lesser amplitude or even complete cancellation. This is due to the peak of one wave aligning with the trough of the other, causing them to cancel each other out.

The concept of path difference is fundamental in understanding various phenomena in physics, such as the patterns seen in diffraction and interference experiments, the working of musical instruments, and the formation of colours in thin films and bubbles. It is also essential in technologies like interferometry and holography, which rely on the interference of light to produce images or measurements.

In summary, the path difference is a key factor in determining how waves interact when they meet. By understanding this concept, you can predict and explain the behaviour of waves in a variety of situations.