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I had never heard that phrase before. Here is an article about techniques of public speaking which uses the term in context.
It seems that βsounding periodsβ is a type of lofty and maybe pompous rhetorical flourish. Such turns of phrase will alienate practical or less educated people who are either annoyed by pretension or canβt understand the phrasing at all. Sermons must be delivered so that all hearers may understand the meaning.
A quote from the article TestDEN: Chapter XXI. Influencing By Narration:
It will be noticed, too, that the literary style in platform narration is likely to be either less polished and more vigorously dramatic than in that intended for publication, or else more fervid and elevated in tone. In this latter respect, however, the best platform speaking of today differs from the models of the preceding generation, wherein a highly dignified, and sometimes pompous, style was thought the only fitting dress for a public deliverance. Great, noble and stirring as these older masters were in their lofty and impassioned eloquence, we are sometimes oppressed when we read their sounding periods for any great length of time - even allowing for all that we lose by missing the speaker's presence, voice, and fire. So let us model our platform narration, as our other forms of speech, upon the effective addresses of the moderns, without lessening our admiration for the older school.