How can you visualize sounds/music?

What are the forms of sound imaging? Sound is an acoustic wave - so you can probably show a simple sound as a wavy line. But most sounds in life are a mixture of these waves of different frequencies and sources. How to visualize something like this?

I guess there are such "visualizers" (what's it called?) typically entertaining - already prehistoric Winamp offered such functions when playing music.

But are there any professional, professional terms for these things? Are there any standards for this field?