AM radio, the scratchy medium that long ago aired Franklin Delano Roosevelt’s fireside chats, soap operas and the day’s most popular music, is trying to avoid becoming static. Across the country, stations are vying to hold on to listeners as AM radio’s audience slowly dwindles. The persistent technology, long dwarfed by FM, has weathered more recent threats including satellite and Internet radio. It is also contending with a new assault from smartphones.