“I still listen to the news every day on WNYC and send them my money,” said Mr. Glass, who is an editorial adviser on “Serial.” “I hope that this is a good thing for public radio in the long run, because if you think of the number of shows that came out of NPR and its affiliates, it’s pretty impressive.” He added that stations that produced innovative original programming would thrive in a digital environment that offers more ways to reach audiences.

If there were no public radio, there would be no WBEZ in Chicago, where “This American Life” began, which means there would be no offshoot like “Serial.” When you listen to Ms. Koenig slowly heating up a cold case, doing interviews that are built on conversations, not sound bites, and taking up to an hour to unfurl a single episode, you are getting aesthetic storytelling that feels like the best of public radio.

But public radio was not what I was listening to last Thursday, and therein lies the problem for shows like NPR’s “All Things Considered” or American Public Media’s “Marketplace.” For the time being, part of my mindshare belongs to Ms. Koenig and her riveting exploration of a terrible event that took place among a group of friends at a Baltimore-area high school.

Charles Kravetz, the general manager of the public radio station WBUR in Boston, which produces original programming including “Here and Now” and “On Point,” is a fan of “Serial.” He can’t help being excited and worried at the same time.

“When you talk to young people, they will tell you that they are listening to a lot of public radio, but when you probe more, you find out that they are listening to podcasts,” he said. “Public radio audience, after years of steady growth, is off slightly, probably in part because people are listening to on-demand programming on podcasts.”

As part of an effort to get its arms around a changing landscape, WBUR received a grant from the Knight Foundation this year to set up BizLab, which will explore new models for public radio. “We have a great, thriving legacy audience and we have to find a way to disrupt ourselves,” Mr. Kravetz said.

Just as web-enabled television viewing took off when the technology became reliable, music programming like Pandora and Spotify gained traction when streaming became routine. I happily pay Spotify for its seemingly infinite array of music — Taylor Swift is a little less satisfied with the arrangement. And after dismissing podcasts for years, I am now dialed in, not just to “Serial,” but to other digital programming like “My Brother, My Brother and Me,” a funny Q. and A. show, and “StartUp,” a series hosted by Alex Blumberg, a former producer for “This American Life” and a founder of NPR’s “Planet Money.” The show chronicles his efforts as a nonbusiness person to start a business — Gimlet Media — that is working on a model to, wait for it, create and make money from podcasts.