Two dippers touch the water of a ripple tank in step…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
Two dippers touch the water of a ripple tank in step. Each sends out ripples of wavelength , and each ripple alone has an amplitude of near the middle of the tank. Point P is from one dipper and from the other. Point Q is from one and from the other. Find the path difference at P in wavelengths, and the amplitude of the water at P and at Q.
Need a reminder? The key ideaShow
Superposition: where waves meet, their displacements add, . Two waves of amplitudes and with a phase difference give ; for equal amplitudes, . A path difference is a phase difference . Intensity .
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.
At P. . In wavelengths, . Two and a half wavelengths is a phase difference of , so the ripples are out of phase. They cancel: . The water at P hardly moves.
At Q. . The ripples are in phase: .
Answer: wavelengths, at P and at Q. We take the two amplitudes as equal at P and at Q. That is close to true when the points are far from the dippers compared with their path difference.
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