Check this Applet tooClick here for details of a CD of these applets
As the applet starts, you see a vibration which begins at the left end traveling towards right. If you observe any particle you would find it vibrating up and down. You would say to yourself, something is moving to the right here, it is not the particles, they are only vibrating up and down - it is a shape or a vibration that is moving to the right- being passed on from particle to particle. That is what wave motion is - a moving vibration or a moving shape.
Why does a vibration move, get passed on - It is because particles are not independent. If you do something to one particle, its neighbour reacts- Here each neighbour behaves the same way as its predecessor, but with a time lag. If all the particles were rigidly bound, then they would all vibrate together- there is no passing on - no shape moving- no wave motion, because they all vibrate simultaneously. And if all the particles were independent, then again a vibration produced will be confined to the particle that is disturbed. There is no wave motion. That shoud define a wave- A vibratory disturbance propagating in an elastic medium.