Ilka and Joby stretch a long rope between them. Each flicks one end upward, and two pulses race toward each other.
The pulses are about to meet on the same piece of rope. One rope cannot hold two shapes at once. So what shape does the rope take where the pulses overlap?
Ilka's pulse, on its own, would lift one point of the rope 2 cm. Joby's pulse, arriving at the same point, would lift it 1 cm on its own.
While the pulses overlap, that point rises 3 cm, because 2 + 1 = 3. The rope adds the two displacements.
The overlap lasts only a moment. Then the two shapes separate.
After they separate, each pulse keeps its own shape and its own direction of travel, as if the other pulse was never there.
This rule is called the principle of superposition.
The rule covers any two waves in any medium, not just two pulses on a rope.
Two pulses overlap on a clothesline. Alone, one pulse would raise a point 4 cm, and the other alone would raise the same point 2 cm. What is the point's displacement while they overlap?
The rope adds the two displacements at that point.
4 + 2 = 6
While the pulses overlap, the point's displacement is 6 cm.
After the two clothesline pulses separate, how does the taller pulse compare with the taller pulse before the overlap?
The waves pass through each other unchanged.
It has the same shape, the same size, and the same direction of travel as before the overlap.
Two pulses on a garden hose meet, overlap, and separate. After they separate, what happens to each pulse?
Two crests overlap at one point of a rope. Alone, one crest would raise that point 7 cm, and the other alone would raise it 5 cm. Enter the point's displacement while they overlap, in cm.
Kerstin says: 'While two waves overlap, the displacement at any point is the two individual displacements added together.' Is Kerstin correct?
Two pulses travel toward each other on a long spring and overlap for a moment. What is the spring's displacement at each point of the overlap?
On a pond, a big ripple and a small ripple pass through the same patch of water and move apart. What does the big ripple look like after the overlap?
Lazlo sends a pulse along a garden hose while a pulse from the far end comes toward it. The hose shows one combined shape for a moment, and then both pulses reappear and carry on. Why do both pulses reappear?