When Two Pulses Meet
Classical Mechanics
Level
2
Two friends are each holding one end of a rope. They give a slight jerk in opposite directions to produce pulses, as shown. When the two pulses meet, they cancel each other out.
What happens next?
The pulses destroy each other and the string remains straight
The pulses reemerge and move on as if they never met
The pulses are reflected back
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1 solution
The superposition of the pulses in this problem is called Destructive Interference (overlapping displacements in opposite directions), and in this case it is perfect; However, contrary to the name, the pulses are not destroyed when they overlap. Nor do they reflect back off each other.
The pulses are opposite transverse displacements travelling in opposite directions - an upward displacement travelling from left to right, and a downward displacement travelling from right to left - and each pulse manifests by the transference of energy ( which cannot be destroyed ).
This means that although the net effect is zero at one particular moment in time, the energy of the upward displacement continues travelling from left to right, and the energy of the downward displacement continues travelling from right to left.
The waves produced in water, sound, and even light exhibit the same behaviour.