I read that as a general rule, the last content word of a phrase gets the most stress. So, in the sentence "I'm late" late will get the most stress. Now if we add the word "Sorry" at the beginning of the sentence "Sorry I'm late" will the word "sorry" change the stress of late? Do we need to stress both the word "Sorry" and "late"? Any suggestion appreciated. Thank you!
To put the main stress of a phrase on the last main stress of the last word or phrase in the phrase was called the "nuclear stress rule" for English in a very influential article by Chomsky, Halle, and Lukoff in 1956. It's a good rule, as such rules go, but there are many exceptions. I think the main stress of "Sorry I'm late" could have the main stress on "late", conforming to the NSR, but the main stress might perhaps go on the first syllable of "sorry", instead. (What I just called "main stress" is also called "primary stress" and annotated with a raised "1", with lesser stresses marked with higher digits "2", etc.)
We like to put a special musical stress called the NUCLEUS (sometimes called the TONIC) on the last new content word in the sentence. By content word we generally mean nouns, verbs, adjectives, adverbs and wh- question words. Most negative words like not and so forth are also usually stressed. The kinds of words you learn in grammar lessons: pronouns, auxiliary verbs, prepositions determiners and so forth are usually unstressed as a rule of thumb. By new content word we mean w rod or concept that hasn't been being discussed yet.
The nucleus is sometimes the loudest syllable in the sentence, but not always. It has musical prominence in that the pitch will be markedly different from what came before it. Nucleuses in English also have their own special musical tone which starts on the nucleus and continues to the end of that intonational phrase (an intonational phrase is like a musical sentence, a musical chunk as opposed to a grammatical one).
It is a mistake to think that the nucleus should be louder than the other musical stresses (formally known as ACCENTS) in the sentence. Very often the first accent in a sentence will be the loudest.
In the phrase Sorry I'm late, whether late takes the nucleus or not will probably depend on whether it's taken as already given from the context that you're late. In other words late here may have the status of old and not new information. It may therefore be de-accented. It would be quite common to hear this with the tonic on the first syllable of sorry, perhaps with a fall-rise nuclear tone.