Why waves propagate so slowly into smooth patches of water

The morning I went to Heligoland I spent some time in the port of Hamburg, trying to film a phenomenon I had recently chatted about with the author of this inspiring guest post: How waves seem to propagate super slowly into smooth patches of water. It turned out to be really difficult to film (because ships didn’t go where I expected them to go [you see me walk a couple of steps half way through the video below, because I needed to get away where a boat was docking], other ships cross the water you are filming, and because filming water is pretty difficult in general).

Here is my best attempt:

So why does it seem to take waves so surprisingly long to propagate into smooth patches of water? Well, because what we see and notice is the phase speed of waves, with which the crests propagate. But the wave field itself only propagates with group speed, which is half the phase speed. So from the movement we notice, waves should be invading the smooth patches twice as fast as they actually do!

Now I need to go and find a good way to film this phenomenon…

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