Whistling kettle mystery solved!

As steam comes up the kettle's spout, it meets a hole at the start of the whistle, which is much narrower than the spout itself. This contracts the flow of steam as it enters the whistle and creates a jet of steam passing through it. The steam jet is naturally unstable, like the jet of water from a garden hose that starts to break into droplets after it has travelled a certain distance. As a result, by the time it reaches the end of the whistle, the jet of steam is no longer a pure column, but slightly disturbed.