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Two equal waves of amplitude 0.40 m run along a rope…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Two equal waves of amplitude m run along a rope. What is the amplitude of their sum when they are in step, and when they are half a wavelength out of step?
Need a reminder? The key ideaShow
Waves add point by point: y = y1 + y2. Two frequencies close together give beats at a second. A string fixed at both ends has and nodes half a wavelength apart. A square wave is a sum of odd harmonics .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. In step. Crest meets crest, so the displacements add: m.
Step 2. Out of step. Crest meets trough, so the displacements cancel: m.
Answer: m in step, and m half a wavelength out of step.
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