If 2 wave trains, launched at the same moment in time, travel the same distance to reach the same point, they will arrive If one has farther to travel, it will arrive a bit late (out of phase) in phase and interfere constructively

If one wave train has farther to travel one-half wavelength further to get to point P, the two waves will arrive P 1)in phase 2) 45 o out of phase 3) 90 o out of phase 4) 180 o out of phase 5) 270 o out of phase 6) 360 o out of phase and interfere 1) constructively2) destructively

4) 180 o out of phase By the time the wavefront from the right arrives at point P, the wavefront from the left has already reached and passed point P, extending ½ wavelength beyond. Its 1 st trough will overlap with the other wave’s crest. Its crest follows, meeting the other wave’s trough. Each portion of the wave from the right will always be ½ wavelength out of phase with the waves from the left…this will continue to be a node. 2) destructively A path length difference of ½ wavelength means the Waves that meet at P will always be 180 o out of phase.