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Water in the kettle is heated until it comes to a boil. The boiling water creates steam and pressure within the kettle.
As the water continues to boil, more steam is created. Because there is limited room within the confines of the kettle, pressure begins to build. More and more steam is being created, but it has nowhere to go.
When the water has boiled long enough to create a lot of steam and pressure, the steam begins to escape through the hole in the top of the kettle. This may happen slowly at first, but as more steam is created faster than it can escape, pressure pushes the steam to flow through the hole faster. Eventually the steam is rushing through the hole so fast that it produces vibrations, causing the kettle to whistle.