Strange water pressure
I had a similar situation as of lately. There are usually only a few things it can be.

1) Cracked pipe and that usually occurs outside from the well to the house. 

2) The pump is bad or giving out.

3) Well is running low and pump needs to be lowered or redrilled.

4) There is too much air pressure in the tank and it needs to be released. 

I do not think it is 1 or 3 because you said no sediments in the water. 
The the noise you hear is probably the well kicking on and off which points to 2, 3 or 4.
In my case it was initially too much air.. after time it was pump need to be lowered. Next, will be drilling lower. Cheers