e.g.The sound was from an iceberg which was breaking up.

(What is the meaning of 'up'? Does 'up' mean 'completely'? Can we use 'breaking' without using 'up'? And does 'breaking up' mean 'melting'?)

You need to learn about phrasal verbs:

http://grammar.ccc.commnet.edu/grammar/verbs.htm#phrasal (Be sure to click on the word HERE to see very useful lists of these verbs.)
and
http://www.eslcafe.com/pv/

And here are several dictionary definitions of this particular phrasal verb, "break up":
http://www.google.com/search?hl=en&rlz=1C1GGGE_enUS379US379&q=define+break+up&oq=define%3A+break+up&aq=0&aqi=g1g-v2&aql=1&gs_sm=c&gs_upl=9087l9762l0l12420l3l3l0l0l0l0l281l753l0.1.2l3l0

Let me know if you have more questions about phrasal verbs or this phrasal verb in particular.

English is a great language. You can chop a tree down, and then chop it up.

In the phrase "breaking up," the word "up" does not mean "completely." Instead, it is part of the phrasal verb "breaking up," which means to separate into smaller pieces or to disintegrate.

When we say "breaking up," we use both words together because that's how the phrasal verb is formed. Using only "breaking" without "up" would change the meaning of the sentence. In this context, "breaking up" implies that the iceberg is breaking into smaller pieces rather than melting.

To understand the meaning of words or phrases, it's helpful to consider the context in which they are used. In this case, the sound was coming from an iceberg, and the phrase "breaking up" indicates that the iceberg was breaking into smaller pieces or fragments, possibly due to external forces like waves or temperature changes. It does not necessarily mean melting, but rather the physical separation of the iceberg into smaller chunks.