You claim that the metal walls of the cooking chamber in a microwave oven protect us from the microwaves. How can they protect us from microwaves when they aren’t even able to keep sound contained? You can hear popcorn popping through the walls. — RB, Beltsville, MD
The fact that sound waves can pass through the cooking chamber’s metal walls doesn’t mean that microwaves can. These two types of waves are very different and the chamber’s walls handle them very differently.
Any type of wave will partially reflect from a surface if passing through that surface causes the wave’s speed to change or, more generally, introduces a change in the “impedance” the wave experiences. Impedance is a quantity that relates various parts of a wave to one another—it relates pressure to velocity in sound and it relates the electric field to the magnetic field in a microwave. Since both sound waves and microwaves change speeds and impedances when they encounter the cooking chamber’s metal walls, they both partially reflect. The sound that you hear when popcorn pops inside the oven is slightly muffled because the sound is having some trouble escaping from the cooking chamber. However, the impedance change for the microwaves is so enormous that the reflection is complete. No microwaves at all escape from the cooking chamber! The same effect occurs when you hold a large mirror up in front of your face. You can hear what’s happening on the other side of the mirror because some sound can pass through the mirror. But light is completely reflected and you can’t see through the mirror at all.