Many audio experts and speaker manufacturers say that loudspeakers benefit from a break-in process. Just like all thing mechanical, speakers have moving parts that move more freely with time and effort.
Two components that particularly benefit from a break-in period include the surround and the spider.
The surround (often times made of various types of rubber or foam) is what connects the edge of the cone to the speaker basket (see Fig. A). You can typically see this part of the speaker when the speaker grille is removed.