Your toilet and water supply lines should not create a humming noise anywhere in your house after you flush the toilet, so when you do hear humming, you need to find the cause immediately. Ignoring a humming noise may lead to serious damage to the plumbing, which can end in water flooding a portion of your house.
Ball Cock Design
If you have an older toilet, the humming noise in your bathroom may be the product of the ball cock assembly in the toilet's tank. The ball cock is the valve that allows fresh water to flow into the toilet's tank after you flush. Because of the design of a ball cock, its valve closes gradually as the float rises in the tank with the rising water level. The changing angle of the ball cock's valve opening can produce a variety of strange noises as well as vibrations. You only need to remove the toilet tank's cover to verify that your toilet has a ball cock assembly, which you can identify by the float sitting on the end of a metal rod that attaches to the top of the ball cock.
Ball Cock Replacement
Newer fill valves found in modern toilets keep their valve open all the way until the float reaches the fill point in the tank, and then the valve closes completely. Replacing the ball cock with a fill valve requires you to empty all of the water out of the toilet's tank. You must close the water supply valve on the wall by twisting its handle to the right as far as you can so the tank does not refill. Flushing the toilet removes most of the water, and then you can sponge or vacuum the rest out. You must undo the water supply line from the ball cock on the underside of the tank and remove the retaining nut before you can insert the fill valve.
Vibrating water supply pipes may cause a vibration sound in your house's plumbing, which you may hear through the toilet as it refills the tank with water. Pipe vibration not only can be annoying, but it may lead to pipe damage as the vibrations split weld joints. A plumber can help you determine what pipes are vibrating and what steps you should take to stop the vibrations, including replacing the water supply valve or installing pipe straps at various points.
Water hammer is similar to pipe vibrations, although it is more violent and damaging to pipes. When the flow of water to the toilet cuts off, shock waves may travel through the water in the supply pipe, causing the vibration sounds. Water hammer can weaken pipe connections, and can even rupture pipes if you do not correct it. A plumber may install an arrestor on the water supply line to stop water hammer, or swap out pipes or valves that are creating the water hammer.