One of the interesting aspects of this poem is its irregular form. If you analyse it closely, you can see that there is no regular meter, rhythm, verse form or rhyme scheme. Rather, the poem is a dramatic monologue of thirty seven lines that are divided into four unequal sections. Each of these consist, in turn, of fourteen, six, eight, and nine lines. Whilst there is rhyme, it is clear that this is not regular, and varies throughout the poem and the different stanzas. Note the way, for instance, that the second stanza has a rhyme scheme of ABACBC, whereas the final stanza has a rhyme scheme of ABBACDDEE. I feel this lack of formal structure helps to express and emphasise the meditative feel of the poem as the speaker seeks to express his thoughts and feelings about what he feels is happening in this world.
The basic rhythm of the poem is iambic, and although the line length is variable, many lines have five feet, so there is a strong suggestion of iambic pentameter in the poem. Lines that best fit this pattern include lines 3, 4, 6, 10, 12, 17, 22, 29, 30, 31, 32, 33, and 34. Arnold takes significant liberties with the form, however, varying rhythm and line length frequently. There are a two-foot line (21), some three-foot lines (1, 23, 28), and some four-foot lines (2, 9, 19, 27). This varying line length gives the impression of smaller and bigger waves washing to the shore.
The author also varies the rhythm often so that it is not consistently iambic. Many lines have extra syllables or out-of-place accents so that the poem tends more toward the rhythms of natural speech than toward a strict metrical cadence. This also is reminiscent of waves--they don't wash in at all the same speed; sometimes a wavelet hurries ahead of or lags behind the larger crest.
In the same way, the stanza lengths vary in size. The first stanza is the largest "wave" that washes in, with fourteen lines, followed by the smallest, with six lines. The third stanza grows to eight lines, and the final stanza swells just slightly to nine lines. We can view this as a weak attempt to follow poetic conventions. Fourteen lines of iambic pentameter make a sonnet; Arnold pays homage to this form without adhering fully to it by having the first stanza be fourteen lines and the next two add up to fourteen lines. However, when sonnets are divided into two sections, they normally break into eight lines first, followed by six; Arnold has reversed that in this poem. Finally, the last stanza is a weak tribute to the Spenserian stanza used in The Faerie Queene, which is a nine-line stanza that uses an ababbcbcc rhyme scheme. Arnold switches that up, using abbacddcc.
Arnold clearly wanted to remain true to some remnants of poetic conventions in this poem while acknowledging the inevitability of change by introducing a great deal of variation into the rhythm, meter, rhyme scheme, and stanzas of the poem.