Matthew Arnold begins his poem "Dover Beach" of describing a beautifully moonlit scene out his window, of the waves crashing on the beach before him. He describes the sea as "calm," the moon as "fair," the cliffs as "glimmering," the bay "tranquil," and the air "sweet." With all of these soothing and beautiful descriptions, one would think that Arnold is enjoying the scene, and taking in the view out his window with tranquility and peace. However, that is not the case at all. Instead, it makes him depressed at the state of the world. Instead of interpreting the scene as happy and beautiful, it reminds him of the misery and unhappiness that exist in the world.
At the very end of stanza one, after describing the beautiful scene before him, he states that
"you hear the grating roar
Of pebbles which the waves draw back, and fling,
At their return, up the high strand,
Begin, and cease, and then again begin,
With tremulous cadence slow, and bring
The eternal note of sadness in."
The key telling line is the last one; he doesn't find the sound of the waves on the rocks soothing or peaceful. Instead, he finds them "grating" and irritating, depressing, and descriptive of "eternal sadness." It brings to his mind the sadness that exists in the world around him; he is reminded of the tragedies that were often in the plays of Sophocles. Sophocles too lived near a sea (the "Aegean Sea") and Arnold infers that because his plays were so sad, the sea must have reminded Sophocles too of "the turbid ebb and flow of human misery." He goes on from this point to launch into a melancholy lament at how all good things in the world have "retreated," just like the waves do, leaving people all alone with misery and ignorance, to try to make it on their own.
I hope that those thoughts help to map out Arnold's thoughts through the poem; good luck!