Older toilets that still have their ball cock and not a newer fill valve can make strange and loud noises after you flush. Understanding what a ball cock does and how it works will help you understand what causes the noise and decide if you want to put in the effort to replace the ball cock with a new fill valve.
Ball Cock Assemblies
Ball cock valve assemblies, used in older toilets, deliver water from the water supply tube outside the toilet to the tank to replenish the water that is released each time you flush. You can identify if your toilet has a ball cock assembly easily by carefully removing the toilet tank's lid. If you see a large plastic float attached to the end of a metal arm, your toilet has a ball cock assembly. The design of the ball cock will produce loud noises, especially as the tank finishes filling and the ball cock's valve is almost closed.
The noise you hear after flushing the toilet may be caused by the ball cock valve's rubber gasket wearing out. The worn gasket will cause the ball cock's valve to seal imperfectly, allowing air and water to escape and creating strange noises. By replacing the rubber gasket with a new one you will decrease the severity of noises coming from the ball cock, but you will not eliminate the strange noises.
Modern fill valves do not operate like ball cock valves. Fill valves have a float, but are smaller and move up and down in the tank. You adjust the height of the float by pinching a clip or twisting a screw on the top of the float. A fill valve will keep its valve open all the way until the toilet's tank fills up to the designated fill point, and then it will close the valve completely. The fact the valve never stays open partway, so creates less noise during operation.
Ball Cock Replacement
Replacing the ball cock with a fill valve will eliminate the strange noises coming from your toilet after you flush. You must drain the toilet's tank by shutting off the water to the toilet, flushing it and then using either a shop vacuum or a sponge and bucket to get rid of the rest of the water. You then undo the nuts holding the water supply line on the bottom of the ball cock and the nut holding the ball cock onto the bottom of the tank, and place the fill valve in the ball cock's place, tighten the nut, and bolt the water line onto the bottom of the fill valve.