Resonance can be observed in the following situation. When two adjacent guitar strings are tuned to the same note and one string is plucked the air vibrations caused by the first string will make the second string vibrate 'in sympathy': if you stop the first string the second will continue to sound. Resonance can also be used to amplify vibrations. Imagine pushing a child on a swing, for example. When you first push, the movements are small, but as you continue to give small regular pushes, each time just as the swing begins its motion away from you, the amplitude of the movement becomes larger and larger - the swing is resonating with your regular pushing motion. Further, you may have noticed that a playground swing will only move back and forth at a particular frequency- its natural frequency - and if you try and push the swing at the wrong moment (i.e., with a different frequency) the amplitude will be decreased.
Helmholtz resonance occurs whenever a volume of air in a cavity is caused to vibrate at its natural frequency, just like when you produce a note by blowing over the mouth of a wine bottle. In this case, the mass of air in the neck of the bottle is pushed away from equilibrium compressing the air inside the body of the bottle, which in turn acts like a spring, pushing the air in the neck and then pulling it back once it travels beyond its starting point. Blowing over the mouth of the bottle tends to reinforce the oscillation of the air at its natural frequency, which is determined by the dimensions of the bottle and the local atmospheric pressure.
