Wave interference is the phenomenon which occurs when two waves meet while traveling along the same medium. The interference of waves causes the medium to take on a shape which results from the net effect of the two individual waves upon the particles of the medium. As mentioned in a previous unit of The Physics Classroom, if two crests having the same shape meet up with one another while traveling in opposite directions along a medium, the medium will take on the shape of a crest with twice the amplitude of the two interfering crests. This type of interference is known as constructive interference. If a crest and a trough having the same shape meet up with one another while traveling in opposite directions along a medium, the two pulses will cancel each other's effect upon the displacement of the medium and the medium will assume the equilibrium position. This type of interference is known as destructive interference. The diagrams below show two waves - one is blue and the other is red - interfering in such a way to produce a resultant shape in a medium; the resultant is shown in green. In two cases (on the left and in the middle), constructive interference occurs and in the third case (on the far right, destructive interference occurs.
But how can sound waves which do not possess crests and troughs interfere constructively and destructively? Sound is a pressure wave which consists of compressions and rarefactions. As a compression passes through a section of a medium, it tends to pull particles together into a small region of space, thus creating a high pressure region. And as a rarefaction passes through a section of a medium, it tends to push particles apart, thus creating a low pressure region. The interference of sound waves causes the particles of the medium to behave in a manner that reflects the net effect of the two individual waves upon the particles. For example, if a compression (high pressure) of one wave meets up with a compression (high pressure) of a second wave at the same location in the medium, then the net effect is that that particular location will experience an even greater pressure. This is a form of constructive interference. If two rarefactions (two low pressure disturbances) from two different sound waves meet up at the same location, then the net effect is that that particular location will experience an even lower pressure. This is also an example of constructive interference. Now if a particular location along the medium repeatedly experiences the interference of two compressions followed up by the interference of two rarefactions, then the two sound waves will continually reinforce each other and produce a very loud sound. The loudness of the sound is the result of the particles at that location of the medium undergoing oscillations from very high to very low pressures. As mentioned in a previous unit, locations along the medium where constructive interference continually occurs are known as anti-nodes.
Information provided by: http://www.glenbrook.k12.il.us