By this period in American history, radio was becoming very important to the entire nation. People would spend their evenings sitting in their living rooms listening to programs, being entertained, and gaining a greater understand of the world around them.
You should tell me what the radio show you chose can reveal about American society at the time. Remember: these shows were created so that people would like them. Their goal is to appeal to people. Therefore, the writers/producers/etc. of radio shows created something they thought people would like, and if the show was popular, that means they succeeded! A radio show (or, for that matter, a novel or movie or TV show or podcast or blog or whatever else it might be) can tell historians what people liked, what people felt comfortable with, and what people’s assumptions were.
Who are the “bad guys” or the “good guys”, if it’s the kind of show that has them? What problems do the characters deal with? What constitutes a “happy ending”? What are the roles of men or women, or people of different races? What are the assumptions the writers are making? If it’s a scary show, what did the radio producers think people at the time were afraid of? If it’s a funny show, what did people at the time think was funny, and would we still think so? If the show you find still has its original commercials, those can be very informative too!