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The interrupter type of electric bell we have for the door bell in general has a small electromagnet with windings wound around it.  The wire of the circuit is connected to a battery via a switch and to the windings and to a long metallic arm which is connected to a spring.  At the end of the long arm, we have a hemi-spherical metallic bell.

When the switch is closed, there is a current in the circuit.  So electromagnet attracts the metallic arm.  Then clapper at the end of the arm hits the metal bell and so disconnects from the circuit. Now there is no electromagnetic force.  So the spring restores it back in contact with the circuit again.  Then again the arm gets attracted due to electromagnetic force.

The frequency of the sound from the bell depends on the electromagnetic force or electromagnet strength.  It is dependent on the current.  The current depends on the battery.  Higher the potential of the battery is, higher the current is.  Higher will be the frequency.  It also depends (directly proportional) on the number of windings and around electromagnet and on the material of electromagnet.