Once you have "The train was frequently ...", you've set up a sentence
talking about something that happens habitually. It's hard to see
how anyone would be able to interpret the sentence as a whole as
talking about something habitual with regard to loudness, but a
one-time event with regard to lateness.
Even separating the two results in something anomalous:
The train was frequently loud, and it was late.
What could that mean? Or, to put it differently, why would a
speaker combine a fact about the habitual loudness of the train with
the fact that it was late on this occasion?
The only interpretation that makes sense is to take
frequently as applying to both adjectives
loud and
late.
Each sentence has its own logic, however, so there may be other cases where the adverb applies only to one adjective.
CJ