Any change in the magnetic environment of a coil of wire will cause a voltage (emf) to be "induced" in the coil. No matter how the change is produced, the voltage will be generated. The change could be produced by changing the magnetic field strength, moving a magnet toward or away from the coil, moving the coil into or out of the magnetic field, rotating the coil relative to the magnet, etc.
An induced current is always in such a direction as to oppose the motion or change causing it
A transformer has two independant coils. When the first coil is energised (Primary coil) with an AC current, it sets up a pulsing magnetic field. This field then cuts the second coil (secondary) and induces an EMF into the second coil. The amount of EMF (voltage) induced inot the second coil wil depend on the supply voltage to the first and the turns ratio of the coils. If there are twice as many coils on the secondary then any voltage applied to the primary will be doubled.
A loudspeaker uses the motor principle to move a paper cone when current from an audio supply travels through the speaker coil.
The paper cone will move backwards and forwards and replicate the magnitude and frequency of the input signal.
When the switch (K) is pressed the coil (E) becomes magnetised and the armature (A) is pulled towards the electromagnet forcing the striker to hit the bell (B). This movement opens the contact T and breaks the circuit therefore demagnetising the coil and releasing the armature. The striker falls. The contact then closes and the process repeats.