Roger R wrote:
snip
The water here is hard and the kettle made a tremendous racket from soon
after getting warm until boiling. As you say the radio could not be heard
above it. Then I started using bottled water and that began to dissolve
the scale, though none could be seen on the element itself except around
where the element is fixed to the vessel. I used a proprietory descaler
to remove all the scale.

Now, using the bottled water it doesn't make any noise at all until just off
boiling, but even then its much less than before. I can hear the radio
again. So I think the noise is made much worse by hardness in the water,
making a very thin - invisible micro scale layer on the element, but why
that should be make the noise worse...? Something to do with the breakdown
of the temporary hardness of the water during boiling perhaps.

With a scaled kettle, the element runs moderately above boiling - as the
scale insulates to a degree.
This means that if a steam bubble forms, and insulates more than the
water, then the scale patch locally heats up to the underlying element
temperature.

Then, when the bubble collapses, the water hits the patch of scale
that's now above boiling.
For a clean metal element, this doesn't happen, as the temperature is
closer to boiling.

My theory anyway.