You wish to design a system to communicate privately with EM radiation inside your home. The communications should not be visible, and people outside of the walls of your home should not be able to spy on them. The system should also be safe for humans. What kind of radiation would be best?

Microwaves

Explanation:

A wave is a phenomenon that causes a disturbance of the particles of a medium  without a permanent displacement of the particles. It transmit energy from one end of the material to another during propagation. It can be classified into mechanical waves and electromagnetic waves.

Mechanical waves are waves that require material medium for their propagation. Examples include: sound waves, wave in a rope, wave in a slinky etc. While electromagnetic waves are waves that do not require material medium for their propagation. They move with the same velocity. Examples are: Radiowaves, X-rays, Gamma rays etc. These waves forms a spectrum, called an EM spectrum.

For the application cited in the question, the appropriate electromagnetic wave that has the required properties is the microwaves. These are usually used in secret communications (satellite) and it is safe for humans.

the answer should be in the picture.