Speakers convert electrical energy into mechanical energy(soundwaves) with magnetism. To understand this process we need answer what is sound. Sound waves are vibrations that pass through a medium. These vibrations are measured in cycles or frequencies(Hertz). High pitched sound has higher frequencies and vice versa. We can hear sound when the sound waves hit our eardrums which convert the energy into electrical signals into our brain. Humans can hear from the range of 20 Hz to 20 kHz, and the diaphragms in the speakers vibrate in this range to produce audible sound.

Most headphones use the moving coil design to produce vibrations in the diaphragm. Electromagnetic induction states that when electrical current goes through a conductor a magnetic field develops around it. This force field interacts with the magnet in the speaker to produce an oscillating motion between the voice coil and diaphragm. So when electrical signal is passed into the headphone a magnetic field is created which interacts with the magnet. The magnets cause the voice coil to move up and down creating vibrations on the diaphragm.

There are other methods to produce vibrations with the diaphragm. All these methods involve magnets and a diaphragm.