How do phase and path difference relate in wave interference?

Phase and path difference are directly related in wave interference, with path difference often causing a phase difference.

In wave interference, the phase difference and path difference between two waves play a crucial role in determining the resultant wave. The phase difference refers to the difference in the phase of two waves at a particular point, measured in degrees or radians. On the other hand, the path difference refers to the difference in the distance travelled by two waves from their respective sources to a particular point.

The relationship between phase and path difference is direct. A path difference of one wavelength corresponds to a phase difference of 360 degrees or 2π radians. This is because one complete wave cycle corresponds to a phase of 360 degrees. Therefore, if two waves have travelled different distances to reach a point such that the difference in their paths is equal to one wavelength, they will have a phase difference of one complete cycle or 360 degrees.

In the context of wave interference, this relationship is crucial. If the path difference is an integer multiple of the wavelength, the phase difference is an integer multiple of 360 degrees, leading to constructive interference. This is when the two waves arrive in phase, their peaks and troughs align, resulting in a wave with greater amplitude.

Conversely, if the path difference is an odd multiple of half the wavelength, the phase difference is an odd multiple of 180 degrees, leading to destructive interference. This is when the two waves arrive out of phase, their peaks align with the troughs of the other, resulting in a wave with reduced or zero amplitude.

Therefore, understanding the relationship between phase and path difference is essential in predicting and analysing the patterns of wave interference. Whether it's light waves creating colourful interference patterns, or sound waves causing areas of loud and quiet, the principles remain the same.