Another perspective on Matthew Arnold's "Dover Beach" involves thinking about the actual geographic setting that Arnold is focusing on, and the symbolic significance of what he sees (or doesn't see).
Dover Beach is located on the southeastern coast of England. The European continent lies to the south/southeast of it. Arnold references this in lines 3-4 by writing "on the French coast the light/ Gleams and is gone." While this is a reference to a specific area, the light is also symbolic of the light of knowledge and progress, of new ideas entering into the world. In this way, Arnold's work takes on a somber tone as the light disappears. The tone is carried on as the narrator finds himself isolated as lines 12-14, describing the motion of the waves which
Begin, and cease, and then again begin,
With tremulous cadence slow, and bring
The eternal note of sadness in.
Stanzas two and three expand on this idea, referring to Sophocles hearing the sound "of human misery" and the following discussion of the Sea of Faith, which
Was once, too, at the full, and round earth’s shore
Lay like the folds of a bright girdle furled.
But now I only hear
Its melancholy, long, withdrawing roar,
Retreating, to the breath
Of the night-wind, down the vast edges drear
And naked shingles of the world.
Arnold combats this tone by ending with apostrophe, focusing the final stanza on a "love," to which the narrator says "let us be true/ To one another." Here the narrator is trying to recenter the focus on things much closer to home that can be looked to for hope and support, as the ideas that once came from elsewhere have dwindled.