Cha-cha has a 4/4 time signature. The first three beats are quarter notes, last beat is two eighth notes, which are emphasized. So you get: one-two-three-CHA-CHA one-two-three-CHA-CHA etc. The beat is up tempo. The mood of the dance is flirty and playful. Search for "cha cha" on YouTube for examples. Another great example of a more current cha cha tune is Santana's "Smooth".
Rumba is a slower, more romantic dance. It is also in 4/4, but much slower. The first two beats are a half note, then two quarter notes. You can think of it the way the timing is for the steps - SLOW, quick, quick where the slow gets two beats. Search YouTube for the tune "Perhaps".
Jive is completely different. It's fast - REALLY fast, danced at 150 bpm or more. The time signature is 2/4, and the basic step sequence is dotted eighth-sixteenth quarter note, dotted eighth-sixteenth quarter note, quarter note quarter note. Or as we think when we dance it, tri-ple step, tri-ple step, rock step. Search YouTube for the song "Runaround Sue" by Dion.
I hope this helps. For any other dance music related questions, let me know.