Interference of water waves 1

Same applet, bigger size

 

Related applets:

Interference 2

Phase Difference

Multiple Sources Interference

Interference of two waves of different frequencies


The interference pattern relies on the wavelength, the source-separation and whether the two sources are in phase or not.
 
Click any point on the interference pattern, the two waves coming from the sources to that point will be shown. The waveforms coloured in blue are equal in their paths of travel and that in red is the waveform along the path difference.

Simply speaking, the kind of interference taking place at P is determined by the phase difference between the the two sources ( the green and the black dots) plus the phase difference because the paths of travel of the two waves are not the same. The blue parts are equal in length, so the latter part arises purely from the red part (the path difference), which is manifested by the vibrations of the black and the red dots (or the green and red if the upper path is longer).

In particular, when the two sources are in phase (phase difference = 0), we only need to consider the phase relationship between the black and the red dots (or the green and the red dots if the upper path is longer) . If the black and the red dots are in phase, a constructive interference occurs at P; but if they are in antiphase, the interference at P is destructive.

In terms of path difference,

constructive interference occus at P when path difference/wavelength = 0, 1, 2, 3, .... , and

destructive interference occurs at P when Path difference/wavelength = 0.5, 1.5, 2.5,...

Don't forget that these conditions are only valid for in-phase sources.

If the two sources are vibrating in anti-phase, the above two conditions will be swapped.