Page "Wave–particle duality" Paragraph 42

In fact, the modern explanation of the uncertainty principle, extending the Copenhagen interpretation first put forward by Bohr and Heisenberg, depends even more centrally on the wave nature of a particle: Just as it is nonsensical to discuss the precise location of a wave on a string, particles do not have perfectly precise positions ; likewise, just as it is nonsensical to discuss the wavelength of a " pulse " wave traveling down a string, particles do not have perfectly precise momenta ( which corresponds to the inverse of wavelength ).

Moreover, when position is relatively well defined, the wave is pulse-like and has a very ill-defined wavelength ( and thus momentum ).

And conversely, when momentum ( and thus wavelength ) is relatively well defined, the wave looks long and sinusoidal, and therefore it has a very ill-defined position.