The pulsating tap indicates that your accumulator (assuming it is positioned near the pump) is not doing its job at all. A working accumulator will act to smooth out pressure variations from the pump.
Test your accumulator is working - from an earlier post on another thread :-
Simple accumulator functional test. Turn off all taps. Turn on pump, wait until pump stops, turn off pump. Turn on a tap and collect the water in a measuring jug and measure how much water you get. If you get about half the volume of the accumulator then everything is set up fine. If you get nothing then either the accumulator is isolated from the system, empty, or there is too much pressure in it. Release some pressure and repeat the test see if that improves things. Adjust the pressure in the accumulator until you get about 1 litre from a 2 litre accumulator.
if nothing comes out then there is no pressure and probably the the air valve has leaked, just pump it up to about 10-15 psi. and test again.