I want a circuit that enbles me to press a button from the ground floor which rings a bell on the first floor and it must operate on 220V AC supply and I have an adaptor. So the supply can be of lower voltage too.
Look for an oscillator. An astable multivibrator will do as well.
When you get the sound, disconnect the battery, and connect the battery to an extra-long wire and connect another extra-long wire to the rest of the circuit, so basically, the battery, the long wire network, and the circuit are all in series. Now there will be two wires exposed. Connect a button to it. Once these wires are touching each other or the button is pushed, the sound goes off.