Exercise 5: Tides.

The earth is not flat but close to spherical. What do long waves look like on a sphere? Imagine that we bend the long wave from above around a sphere:

Its two wavelengths will span the sphere in such a way that there will be two high waters and two low waters. The high waters will be on opposing sides of the sphere, and the low waters will be on opposing sides as well.

This is not what the tidal wave looks like in the real world; but it is an accurate image of the shape of the tide-generating force field. We therefore have to address the tide-generating forces next and shall return to the shape of the tidal wave later.