Answer:
declare
Step-by-step explanation:
The synonym for the underlined homonym "sound" is declare.
A synonym is a word that is similar in meaning with another word, and the word "sound" (as used in the context) is similar in meaning with the word "declare.
This is because the sentence, My father often likes to sound off on the importance of being thrifty means that her father always declares to them that is important to be thrifty.