I just want to make sure I understand the normal modes of a vibrating system of particles with discrete spacing. I have tried to drawn what I understand as the lowest and highest frequency mode of the standing waves. Is the drawing correct? Edit: actually I have drawn the maximum frequency where no particles are permitted to move.. The system is 4 particles and for standing waves their vibrations are described by: y(s) = sin(sKa) with a time dependence and where s refers to particle number s and a is the particle spacing. Now with y(0)=y(4) you have the modes: k=[itex]\pi[/itex]/4a, [itex]2\pi[/itex]/4a, k=[itex]3\pi[/itex]/4a The last one corresponds to no movement of any particle. Is this correctly understood? What happens if we take for instance k=[itex]5\pi[/itex]/4a. Does this mode simply reproduce the motion of k=[itex]\pi[/itex]/4a?