Modelling: Depth of Water in a Tidal River

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This excel file looks at using the sine curve to model the water depth in a tidal river.

The first interactive sheet shows how the Earth’s orbit around the Sun can be modelled by the sine curve. One or two cycles can be displayed. The second sheet shows how the sine curve can model a cycle which takes 24 hours to complete.

The next sheet demonstrates how the depth of water in a tidal river can be modelled. The high tide time, mean water level and difference between high and low tides can be adjusted, and their effects on the model can be seen. The equation of the curve can be shown, and random models can also be generated.

The following sheet contains questions on a set of seven different water depth models. Students can either calculate the equation of the model from given values, or, given the equation, work out the values for each model. The graph for each model can also be revealed and a new set of questions generated each time.

The file also includes five worksheets to be printed off and completed by students. Topics include various transformations of a range of functions, focussing on the sine curve. No solutions are included.

This program was designed by be viewed on a screen with a resolution of 1024 x 768. Users may have to adjust the resolution of their screen for the pages to display as was originally intended. The program uses macros which need to be enabled on users’ machine.

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