## 5. Using transformed sine waves to model real systems

We have demonstrated that a sine wave can be 'customized' to simulate any regular cycle, such as a diurnal or seasonal cycle. You can even combine sine waves, for instance to produce a very crude representation of a monthly tidal cycle:

The spreadsheet-based model in the diagram combines two sine waves. The first simulates the regular cycle of high and low tides (with a period of about 12.4 hours), whilst the second is a longer-period cycle that represents – very crudely – the spring-neap cycle with a period of about 14 days. Note that the curve has not been smoothed out, so it appears jagged as straight lines join data points that are two hours apart. The two cycles were constructed using the same approach used in section 4 to transform a single sine wave.