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Waves are disturbances that propagate through space and time. Classically, they travelled through a medium, disturbing the particles but not changing their mean position. Electromagnetic waves/particle-waves need no medium; they are disturbances in their respective fields.

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Non-standing waves on string

.$$ The problem: this wave function $\psi$ will always be a standing wave, independently of the wavelength, however, experience shows that only $\lambda=n*2*L$ wavelengths generate standing waves. …
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