History: The idea that sounds are made up of sine waves stems from what theory?

The idea that sounds are made up of sine waves stems from what theory?

• Nyquist-Shannon sampling theorem.
  From this theorem stems the idea we need to double the sampling rate of the highest audible frequency.
• Laplace theorem.
  While related...
• Discrete-time theorem.
  There's a better answer.
• Fourier theorem.
  Yes!