Reader Questions

Reader Question: Standing Waves

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captainandry asks:

What would happen to a fish or swimmer in a standing wave?

First of all, check out the video that inspired this question, which shows a standing water wave created in a wave tank. Before we tackle the standing wave, it’s helpful to know what motion exists in a typical water wave. For deep water waves, the motion of a particle as the waves pass is circular, with a decreasing radius with increasing depth. Below a certain depth the energy of the surface wave doesn’t penetrate. Here’s an animation, where the red dots represent massless particles and the blue circles show their paths:

In shallower waters, the circular paths get compressed into ellipses. The image below shows pathlines for particles at different depths as a water wave passes. Notice how the paths are circular near the surface, where the depth is much greater than the wavelength, while close to the bottom, the pathlines are elliptical.

So what about motion for a standing water wave? Such a wave has no apparent horizontal motion, as seen in the animation below:

Similar to the way that decreasing the depth compresses the circular particle motion into an ellipsoid, creating a standing wave compresses the horizontal motion of any particle near the surface. What this means is that anything floating near the surface of the standing wave will simply bob up and down. Unless it’s located at one of the nodes (marked by red dots), in which case it won’t move at all! As with the other types of water waves, the amount of displacement will decrease with depth. People and fish, of course, are not massless particles, so their motion will be damped by inertia, but the same principles apply.

(Photo credits: P. Videtich; R. L. Wiegel and J.W. Johnson; Wikipedia)

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