How can a single ear drume in you ear hear multiple frequencies at the same time?

Sound is a pressure in air and when the pressure waves from multiple sources interact you get the sum of all those waves. So the pressure wave that reaches your ear is a combination of all sound sources and results in a single pressure on your eardrum at each moment in time. Over time the eardrum move following the combined pressure of all the sound waves.

If a force a speaker membrane to move just like your eardrum did it will produce a pressure wave just like the one that reached your ear and you will hear the same sound.

Mathematically you can show that any periodical movment that is just not a single sine wave can be described as the sum of multiple sine waves. So unless it will perfectly move as just a single sine wave it will produce multiple frequencies. You can show the same thing for no period signals but then you can never have a single frequency, if you did it would be a periodic sine wave.