The relative motion of the Earth, Moon and Sun causes water to flow around the Earth. The effect is to produce a high tide approximately twice per day and a low tide approximately twice per day.

This means that the period of a complete tidal cycle is 12 hours. If the difference in the height of high tide and low tide ismetres then the depth of waterhours after high tide ismetres

whereis the minimum depth of water.

In the diagram aboveand

Much of the time people are interested in the depth of the water at a certain time, not the depth of the water so many hours after high tide. To take account of this we must incude a phaseThe depth of water at time t is now(1)

can be found by recording the depth of water at(midnight), and whether the tide is falling or rising. For the diagram belowand the tide is rising.

soandPuttingand solving for t gives t=7.86 hours.