I happen to know the answer to this question (*^__^*) Hehe...
Because I have watched "The Little Mermaid" two or three times. So there is an impression.
First of all, the whole film has a theme song, which is expressed in different ways throughout the film, but it is the same melody. This song is called "Part of your world" and it's the song Ariel sang.
The short paragraph you mentioned is also slightly modified from this song.
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I only found the mp3 of the song sung by the witch, and the short piece of music you want is included in the middle. Then there should be no independently intercepted resources for this small section!
If you want the lyrics of these songs, you can contact me again. O(∩_∩)O~