What is the setting of the first stanza? Who are the speaker and the person being addressed in "Dover Beach"?

The setting of the first stanza is the Straits of Dover, a strait at the narrowest part of the English Channel. It is at the East End of the English Channel where it joins the North Sea. (This is near the location of the Chunnel, the Channel tunnel that runs under the sea from England to France.) The persona, or speaker, is undetermined, but it is probably a man who is speaking to his companion, a woman he loves.

Since Matthew Arnold and his wife honeymooned at Dover Beach in 1851, it is commonly believed that Arnold's first draft of his poem was written near the time he and his wife stood on the cliffs and looked over the English Channel toward France's coast, some twenty-six miles away, where the beacon light of Calais shone. For these reasons, Arnold and his wife are the supposed models of the speaker and his companion. Nevertheless, the couple could be any two lovers, depicted in a pensive moment of their early lives.

Arnold's poem is written as a dramatic monologue, a genre which has only one speaker, but there is a silent audience of one or more persons. Thus, the effect is more powerful than if the speaker were only musing to him/herself. As he peers across to a country which once conquered England in 1066, and that pitted its kings and kingdoms against those of England for over a century (1337-1453, the Hundred Years War), perhaps the speaker senses the notes of sadness to come, such as the ills of the Industrial era of his age, as well as those that already accompany the sea's "melancholy, long, withdrawing roar."