Allan H. Frey was the first American to publish on the microwave auditory effect (MAE). Frey's "Human auditory system response to modulated electromagnetic energy" appeared in the Journal of Applied Physiology in 1961.
In his experiments, the subjects were discovered to be able to hear appropriately pulsed microwave radiation, from a distance of a few inches to hundreds of feet from the transmitter.
In Frey's tests, a repetition rate of 50 Hz was used, with pulse width between 10–70 microseconds.
The perceived loudness was found to be linked to the peak power density, instead of average power density.
At 1.245 GHz, the peak power density for perception was below 80 mW/cm2.
According to Frey, the induced sounds were described as "a buzz, clicking, hiss, or knocking, depending on several transmitter parameters, for example, pulse width and pulse-repetition rate".
By changing transmitter parameters, Frey was able to induce the "perception of severe buffeting of the head, without such apparent vestibular symptoms as dizziness or nausea".
Other transmitter parameters induced a pins and needles sensation.
Frey experimented with nerve-deaf subjects, and speculated that the human detecting mechanism was in the cochlea, but at the time of the experiment the results were inconclusive due to factors such as tinnitus.
Auditory sensations of clicking or buzzing have been reported by some workers at modern-day microwave transmitting sites that emit pulsed microwave radiation. Auditory responses to transmitted frequencies from approximately 200 MHz to at least 3 GHz have been reported.
The cause is thought to be thermoelastic expansion of portions of auditory apparatus, and the generally accepted mechanism is rapid (but minuscule, in the range of 10−5 °C) heating of brain by each pulse, and the resulting pressure wave traveling through the skull to the cochlea.
In 1975, an article by neuropsychologist Don Justesen discussing radiation effects on human perception referred to an experiment by Joseph C. Sharp and Mark Grove at the Walter Reed Army Institute of Research during which Sharp and Grove reportedly were able to recognize nine out of ten words transmitted by "voice modulated microwaves".
Although it's been reported that "power levels required for transmitting sound... would cause brain damage due to... thermal effects" the pops associated with the microwave audio effect are not sustained over time, and the effect is due to brief, sudden, increases in temperature.
So while threshold levels of for the microwave audio effect of 267mW/cm² for 1.3GHz and 5000mW/cm² 2.9GHz, respectively, were reported by Frey in 1961, for the peak amplitude (providing the pops) and would only give an average (sustained) power density of only 0.4mW/cm² and 2mW/cm² respectively similar to current cellphones.
However, it's been argued that despite waves the microwave auditory effect only constituting a rapid 10−6 °C rise in temperature, for threshold peaks on each pulse, that, at the least, a strong peak of around 1400 kW/cm² (1.4 billion mW/cm²) would certainly be harmful due to the resulting pressure wave.
References:
https://www.researchgate.net/publication/251757478_HUMAN_AUDITORY_PERCEPTION_OF_PULSED_RADIOFREQUENCY_ENERGY
https://www.newscientist.com/article/dn14250-microwave-ray-gun-controls-crowds-with-noise/
https://books.google.co.uk/books?id=8iIlDwAAQBAJ&pg=PA125&redir_esc=y#v=onepage&q&f=false
https://web.archive.org/web/20200328184923/https://www.bibliotecapleyades.net/scalar_tech/the_hum/frey.htm
https://www.science.org/doi/abs/10.1126/science.209.4461.1144?sid=f514230e-1373-4da5-ad36-3689f428e21b
