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It's a little difficult to explain this question .. but I'll try anyway.

To the best of my knowledge propagation models - audio, RF - are modelled as travelling in a sinusoidal form. Surely if a model was constructed based on observation, and then verified by experiment the experiment would more often yield the desired result than not.

Is the model for sinusoidal motion/waves deemed true because the equations are proved true by experiment? How do we know these waves are actually sinusoidal? How was this model developed?

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Jean Baptiste Joseph Fourier initiated the investigation of Fourier series and their applications to problems of heat transfer and vibrations. –  Mark Rovetta Jan 10 '13 at 0:09

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The waves are not necessarily sinusoidal, but any description of a function which is integrable (i.e., has a finite area or "energy") can be decomposed into superpositions (sums) of sines and cosines, or alternatively (and equivalently) complex exponentials. This is why they are shown as sine or cosine waves, because that is the simplest object to think about. In reality, they are a (possible infinite) sum of the sine and/or cosine waves.

Also, you can build an antenna, and if you modulate it very carefully with a sine wave electrically, it will radiate a sine wave...

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