As many of Longfellow's poems, The SOund of the Sea takes its inspiration from nature, finding a divine voice in the sound and pattern of the ocean tides.
There are several possible approaches to critical analysis. One is to look at how Longfellow manipulates the conventions of the Italian sonnet -- is there actually a "turn" in the sonnet? If so, what is it?
Next, you could look at Longfellow's approach to the sea as an expression of transcendentalism. Does Longfellow subscribe in this poem to a pantheistic or immanentist notion of the divne?
Finally, it might be worth comparing the tides in Longfellow to the much darker ones in Arnold's Dover Beach, in which the sea of faith is retreating rather than bringing revelation.