What is it called when beginning sounds repeat in a poem?

Alliteration. Alliteration is easy to spot because the first consonant in the sentence is repeated throughout. Alliteration is not only used in poetry, but it can be seen in a number of printed works, including advertising and headlines. It could also appear in someone's name.

The most common modern example we have in names is with the Kardashian sisters. All of their names begin with K, including Kim Kardashian, Khloe Kardashian, and Kourtney Kardashian. They all start with the same consonant, which is the letter K. Another popular example is in characters of the Harry Potter series.

It is called alliteration. Alliteration are always based upon a rhythm. A rhythm simply refers to a back and forth motion. It could be a pendulum swinging, or a beat tapping with fixed intervals. In music and poems however, a rhythm refers to the constant speed with which a musical instrument, a poem, or a song is played.

Each beat in a rhythm refers to a fixed pattern of time intervals and the entire piece of poem or music basically revolves around these time intervals. Alternatively, it could also be referred to as the constant duration pattern of silences in the song or poem.