Lazlo films two pulses heading toward each other on a rope: a crest that would raise a point 2 cm, and a trough that would lower the same point 1 cm. He pauses the video at the moment they overlap.
The principle of superposition names what the rope does where waves overlap: it adds. This lesson uses the rule to work out the rope's exact shape, point by point.
In this lesson, upward displacements are positive and downward displacements are negative.
Lazlo picks one point inside the overlap. The crest alone would put that point at +2 cm, and the trough alone would put it at -1 cm.
The same add happens at the next point, and the next. Each point takes its own sum.
Points under only one pulse are easy: the other pulse contributes nothing there, so the sum is just the one pulse's displacement.
Joining up all the summed points gives the rope's exact shape at the paused instant.
At one point of an overlap, one pulse alone gives +3 cm and the other alone gives +2 cm. Find the point's displacement.
Both displacements are upward, so both are positive.
3 + 2 = 5
The point's displacement is +5 cm.
At another point, one pulse alone gives -2 cm and the other alone gives -3 cm. Find the point's displacement.
Both displacements are downward, so both are negative.
-2 + (-3) = -5
The point's displacement is -5 cm.
Two 4 cm crests overlap at one point of a cord. Enter the point's displacement while they overlap, in cm.
A 9 cm crest and a 3 cm trough overlap at one point of a rope. Enter the point's displacement, in cm. Use a minus sign if the displacement is downward.
A 5 cm crest and a 5 cm trough overlap at one point of a hose. Enter the point's displacement, in cm. Use a minus sign if the displacement is downward.
On a long dock rope, a 12 cm crest and a 5 cm trough overlap at one point. Enter the point's displacement, in cm. Use a minus sign if the displacement is downward.
A 3 cm crest and a 14 cm trough overlap at one point of a clothesline. Enter the point's displacement, in cm. Use a minus sign if the displacement is downward.
Joby finds the displacement of a cord at one point where two pulses overlap. Which method is correct?