Water pump noises

[Drpps]

I have had a search through the threads and can't seem to find an answer to this so hoping someone can help.
When I turn on the tap it runs instantly with good pressure and the pump, pumps with the noise you would expect. When I turn it off there are 5-10 seconds a sort of slow 'pump pump pump' noise (about 2/sec) which often goes again after a 10-15 sec delay for perhaps 5 minutes after using the tap. This is especially noticable at night when my head is near the rear cupboard! It is fairly quiet so only really heard when there are no other sounds.
Is it a pressurised system which once the tap has run is re-pressurising? Is it a valve sucking in air to equalise the pressure once the water has come out?
Please help. The chirrupping low pitched squeak is driving me mad!
Thank you
Paul