The use of "grating roar" and "withdrawing roar" are used in the poem to reinforce the speakers message. What are their effectiveness for each in relation to how the poet creates the poem's meaning.
The central theme in Dover Beach relates to a universal loss of faith. Arnold questions man's loss of belief and is quite cynical about the results brought about by the growth in science and technology during the Victorian Age and the resultant Industrial Revolution. The outcome
Hath really neither joy, nor love, nor light,
Nor certitude, nor peace, nor help for pain
This is the point he wishes to make by using the evocative images of nature, specifically the ocean, metaphorically utilising its continuous ebb and flow to illustrate man's alienation from belief.
The first stanza paints a beautiful and invigorating scene of nature at work. The speaker is impressed by nature's abundance, however, in line 9 we become aware of a hint of negativity:
Listen! you hear the grating roar
Arnold not only effectively uses onomatopoeia to describe the sound made by the pebbles as they are drawn back and flung out by the waves, but also suggests that the sound is jarring (grating). In this sense then, there also exists some imperfection in nature - its tranquil nature has a disturbing element to it. The point is emphasised in the last two lines of the stanza:
With tremulous cadence slow, and bring
The eternal note of sadness in.
It is clear that all is not well with the world. The speaker is saddened when he listens to the sounds created by the ocean. It is, as far as the speaker is concerned, a profound sadness for, in his perspective, it is eternal. The speaker is at this point, quite cynical about the nature of things - a situation which seemingly, will never be resolved. In this sense then, 'the grating roar' is a disturbance, an anomaly in the otherwise perfect nature of things.
Arnold uses the metaphor, "The sea of Faith" and equates it with the regularity found in nature - the constant and eternal ebb and flow of the sea. Now, though, the poet is saddened since in the sound of the ocean he only hears:
Its melancholy, long, withdrawing roar,
He believes that man's faith (spirituality) is fast disappearing and he is despondent that man would stand naked, indefensible against the ravages of the world since he has withdrawn from believing. Man has become a victim of his loss of faith and has become vulnerable. The point is emphasised by the use of terms such as 'night', 'drear' and 'naked'.
Finally, in the last stanza, the speaker, in order to find some resolution, asks his love that, amidst such confusion and negativity, that they should be true to each other (for they would not find such truth in the world).