Well, one of the easiest and simplest ways to demonstrate the formation of waves is to hold the loose end of a rope which is fixed at the other end and to move it quickly up and down. Crests and troughs of the waves advance towards the fixed end of the rope. If the rope is very long, we can observe such a crest or trough. For the formation of progressive waves, we have a long unlimited rope , but if the medium is limited, of finite extent as we have in the case of a violin having a small string, fixed at both in ends, an interesting thing happens. 

The progressive waves traveling on the string will get reflected at both fixed ends. Due to the superposition of incoming and reflected waves along the string results in the formation of standing waves. Standing waves or stationary waves are therefore formed /produced by the simultaneous transmission of two identical wave motions in opposite directions. Remember, we are talking about the mechanical waves. EM- waves like radio-waves, X-rays, light waves etc. are a class of their own and can travel even without a material medium. Mechanical waves are of two types:-

1) Transverse waves - are the waves in which the vibration of displacement takes place in a plane at right angles to the direction of propagation of the wave. Even non -mechanical waves are transverse in character. Waves on a stretched string are of this type only, as also the waves produced in a string.

2) Longitudinal waves-  are the waves in which the vibration or displacement take place in the direction of propagation of the waves, sound waves and waves in a long spring the free end of which is pulled or pushed along its length fall in this category.