The figurative or symbolic meaning that Sophocles might have found in the sound of the waves crashing on the shore is as Arnold states it--"human misery and woe," and notes of "eternal sadness." Waves cannot literally usher in human misery or melancholy, but as Arnold looks upon the moonlit beach before him, he draws his own conclusions about the sound of the waves. To him, they sound sad, and Arnold's rather pessimistic world-view of the earth being a place where goodness has fled, comes into play for his interpretation of what that sound is. He then mentions that Sophocles must have had the same reaction--he bases this on the fact that Sophocles wrote plays that were filled with a lot of awful human suffering. Arnold infers that in order for Sophocles to do that, he too must have seen the world as a miserable place, and hence tied the sad sound of waves to that misery also.
A more literal sound that Sophocles might have heard is the sound of war upon the waves as armies and battles fought it out, just as Arnold mentions in the third stanza, that "ignorant armies clash by night." War existed in ancient times also, and like always, was a disheartening thing to witness, one that often led people to lose their faith in god mankind.
I hope that those thoughts helped; good luck!
These are the lines from Arnold's elegiac poem, Dover Beach you refer to in your question :
Sophocles long ago
Heard it on the Aegaen, and it brought
Into his mind the turbid ebb and flow
Of human misery, we
Find also in the sound a thought
Hearing it by the distant northern sea.
Arnold, looking at the nightscape of the Dover sea--the 'moon-blanched' sandy shore, 'the long line of spray', the image of the moon on the straits, the glimmering light on the French coast, the upcoming & retreating waves--and listening to harsh frictional noise of pebbles in the tides, remembers the ancient Greek tragedywright, Sophocles, who must have also heard the same 'eternal note of sadness' in the tides of the Greek sea, as Arnold hears in the Dover sea in the middle of the 19th century.
The lines show a literal as well as a symbolic switch to the past from the present. Arnold, an avid reader and admirer of Classical Greek literature, writing an elegy on the tragic decline of faith in the world of man in an age of Industrialism, finds proximity with Sophocles. At the heart of Sophocles's tragedies was a deep perception of 'the turbid ebb and flow/Of human misery' which his successor can still hear in a different time and space. The auditory image of the 'grating roar' in the perpetual movement of the sea-waves brings into the mind of the English poet of the Victorian era an 'eternal note of sadness', and it was not unknown to the ancient writer of tragedies. Thus Arnold believes that he himself and his illustrious predecessor were both artists working out universal tragic predicament.