I'm trying to understand how can multiple radio stations transmit information just by transmitting using different frequency. The way I understand it all those different frequency waves add up to a single wave? If so how can that not corrupt information on other frequencies?

Say if I transmit: sin(2pix)

And separately: sin(2pix*2)

Does it end up as a single wave of: sin(2pix)+sin(2pix*2) ?

Or does it work in a different way completely?

Thank you!

I'm trying to understand how can multiple radio stations transmit information just by transmitting using different frequency. The way I understand it all those different frequency waves add up to a single wave? If so how can that not corrupt information on other frequencies?

Say if I transmit: $\sin(2\pi x)$

And separately: $\sin(2\pi x\times 2)$

Does it end up as a single wave of: $\sin(2\pi x)+\sin(2\pi x\times 2)$?

Or does it work in a different way completely?