Thunderheads over the Straits of Florida send crackles of static across the radio signals, but as the dial spins down the AM band through the Cuban capital's blend of pop music, propaganda and sports reports, WTOP from Washington, D.C., announces beach traffic conditions on the Bay Bridge.

For several minutes, the late-evening WTOP news comes in loud and clear with President Reagan's tax-bill problems, then it fades away beneath a growing electronic hum as the broadcaster turns to Polish protests.

Whether this was coincidence or jamming could not be determined immediately, but even as WTOP faded away, half a dozen other American commercial stations came in clearly.

This casual penetration of Cuba's airwaves began long before Fidel Castro took power. Its effect is debatable. Some people say this conveyance of the American dream is more subversive to Castro's shortage-ridden revolution than anything the proposed U.S. Radio Marti might offer.

In any case, the Americana comes in--most of it in English, but some from the Miami area in Spanish. Technicians here can rattle off a dozen or more U.S. stations easily picked up on Cuban AM radio sets.

As I dial down the band on my little battery-powered Sony, a Southern evangelical preacher brings me the message of Moses and the Burning Bush.

Then Miami's WGBS reminds the radio audience of how Americans loved "My Favorite Martian" and "The Patty Duke Show" back in 1963, a year Cubans tend to remember more for the aftermath of the missile crisis.

Deputy Foreign Minister Ricardo Alarcon said he particularly likes WGBS, which he can hear "perfectly well" in his house. Although he does not listen "regularly," he said, he often picks up its weather reports.

"The quality of transmission is incredible," Alarcon said. "I don't like to listen to the Voice of America. Radio Marti will be the same. If I'm listening to the commercial stations I want to hear nothing but music, the news flashes, that sort of thing."

In fact, the AM broadcasts of the U.S. government's Voice of America, which is supposed to present balanced reporting rather than propaganda, are jammed in Havana. Diplomats here note, however, that the buzz of the jamming makes the station easier to find.

I could not pick up Miami's WQBA, offering "Cubanissima" in Spanish to Florida's Cuban-exile community. Some diplomats say it is heard attentively by many Cubans here, but one official noted that its reports of supermarket sales, ads for Miami banks and reports on Dade County politics "are like sending a message that people here don't know how to decode."

One station must seem particularly indecipherable, even to Cuba's English speakers: "The Music Country Network" beamed from Nashville's WSM, by satellite, to subscribers all over the United States. The disc jockey plays a country hit that, on this late Havana night, could apply to attitudes encountered on both sides of the water as the prospect of a "radio war" also looms over the Straits of Florida: "May the Bird of Paradise Fly up Your Nose."