Microwave strikes may have been responsible for the sonic delusions and real brain damage suffered by embassy staff and family members in Cuba and China. Starting in late 2016, more than three dozen American diplomats and family members have reported the baffling symptoms and ailments. The State Department says its investigation had yet to identify the cause or source of the attacks.

Strikes with microwaves plausibly explain reports of painful sounds and brain trauma associated with the embassy attacks. Microwaves are a form of electromagnetic radiation on the same spectrum as light and X-rays, only at the opposite end. They’re seen as harmless in such everyday uses as microwaving foods, but when tightly focused, they can form a powerful beam. Using these beams as a weapon can disable attackers and wage psychological warfare.

Douglas H. Smith, director of the Center for Brain Injury and Repair at the University of Pennsylvania, said in a recent interview that microwaves were now considered a main suspect in the embassy attacks. He was one of the original medical team that examined 21 affected diplomats from Cuba.

Allan H. Frey, an American scientist, found that microwaves can trick the brain into perceiving what seem to be ordinary sounds.A defining symptom of the diplomatic incidents was the perception of loud noises, including ringing, buzzing and grinding. Mr. Frey said federal investigators have spoken with him in an effort to solve the puzzle.

Russia, China and many European states are seen as having the ability to make basic microwave weapons. Only intelligence agencies know which nations actually possess and use such arms. The American military has sought to develop microwave weapons that could invisibly beam loud sounds or spoken words into people’s heads. The Pentagon has released a video of its Active Denial System, which fires an invisible beam meant to deter criminals with fiery sensations.