When sound waves are produced, the greatest displacement of particles in a medium around their mean location is known as _____.

The maximum displacement of the particle on either side from the mean position is known as the amplitude of the wave.  It would be either a crest's or a trough's highest point.

 The crest is the point on the wave with the maximum value on the positive side of the wave. A trough is a point on the wave with a minimum value on the negative side of the wave.