Notice how short some of the sentences are in "Morning Song"? They force you to pause – often in the middle of a line. That sort of choppiness might not seem immediately apparent when you're looking at the lines on the page, but reading the poem aloud will immediately make these pauses come to light. They help to build the sense that the speaker's worldview right now is chaotic, suddenly shifting, and generally emotionally charged.
Even though there's no overt rhyme scheme in this poem, Plath plays with assonance (the repetition of a vowel sound) in several stanzas of this poem: check out the way that short a's (in bold) and long a's (in italics) repeat in this stanza, for instance:
Our voices echo, magnifying your arrival. New statue.
In a drafty museum, your nakedness
shadows our safety. We stand round blankly as walls.
And let's not even talk about the way that "new," "stat-ue," and "mu-seum" all repeat "ew." Or how the diphthongs (a fancy term for smashing two vowel sounds together) in "our" and "your" are each repeated twice in the stanza.
Such dense overlapping of vowel sounds tends to perform the echoing effect that speaker says "our voices" have created. It's almost as if the poem itself enacts its subject matter – which makes the intense personal message of the poem even more realistic. It's not an emotional appeal to a new baby that's cleverly wrapped in elaborate rhyme schemes or iambic pentameter. Nope, Plath's assonance is much more subtle than that, creating interwoven vowel patterns which seem as natural as your normal speaking voice.