Yes, you can actually hear microwave pulsesS

In the 1940s, when World War II was in full swing and radar transponders were military equipment to which many people were exposed, the personnel who worked with them reported hearing a clicking noise. The noise, oddly, always seemed to be inside or directly behind their head, no matter which way they were oriented with respect to the source of the microwaves. At first people looked for clicking equipment, because the idea that the microwave pulses themselves were making the sound was silly. Microwaves can't make a sound, because they're part of the electromagnetic spectrum. It would be like hearing the color red. So what was happening around those dishes? Basically, physics was getting Zen.

A tree falling in a forest cannot make a sound (as in the noise perceived by the brain in response to the ear), unless a human is there to hear that sound. An ear, then, should be able to make a sound without any physical object making the air vibrate. Instead of moving air, people were hearing the microwave auditory effect. The inner ear has sections that are filled with air, and sections that are filled with fluid, and all of those sections are vulnerable to microwaves. Microwaves do exactly what the microwave in your kitchen does - heat things up. As they heat, they expand, and shift. The slight expansion can't be felt anywhere else in the head, but the ear is designed to monitor the shifts inside these spaces, and interprets them as sound.

People have found that the loudness of the sound corresponds to the power of the of the microwaves. As for the audible frequencies, people could hear anything between two hundred million and three billion cycles per second. Ever since the mystery was explained fully, researchers have been working on ways of tweaking this concept to make weapons or secret communication systems. A microwave that could give coded messages to a spy, or a weapon that creates a loud buzzing or clicking which might disperse a crowd has been much in demand. So far, nothing has come of the research. Except a better understanding of koans.

Image: Graham Shaw

Via Princeton, NCBI, Wired.