I don't know what is causing the knocking, but you'd better acquaint yourself with pipe sizes. I think it's most likely that you have 3/4" pipe that is then reduced to 1/2". Even if 1/4" was made in ridged pipe, that would be far too small for a washing machine. !/4" soft copper is often used for ice maker supply lines. One thing you might check is the washer shut off valves. Make sure they are turn completely on. I'm sure some of the pros will give you some better answers, but it may be tomorrow before some of them are online.