Acoustic Waves in a 2D Numerically Modeled Solid In this simulation the bonding is done with a Lennard-Jones (LJ) potential. LJ potentials have extremely large repelling forces when the particles get too close and longer range attractive forces when the particles are farther apart. The LJ potential is of the form V(r)=4VLJ[(sigma/r)^2b-(sigma/r)^b] where V is the potential minimum, sigma is a scaling parameter, r is the particle separation, and b is an integer that is adjustable by the learner. The larger the value of b, the more abrupt is the force change with distance, r. The solid is set up so that all the particles are separated by an r that causes the nearest neighbor forces to be zero. An obvious result of that set up is that alternate rows of particles have to be staggered by 1/2 spacing in the horizontal direction and the vertical spacing of rows is squareroot(3)/2 times the horizontal spacing of particles in any row. The longitudinal acoustic wave is initiated by oscillating the vertical position of the top row by a given amplitude at a selected frequency. The transverse acoustic wave is initiated by oscillating the horizontal position of the top row by a given amplitude at a selected frequency. The details of the resulting waves in the rest of the solid are shown by plots of both the displacement sums of either the rows (blue) or the columns (green). For a stable solid, it is seen that about 40 rows are required to see a full wavelength of displacement. Since 50 rows is about one wavelength, lambda, and wave speed is frequency*lambda that means that the wave speed is about c=w0*40*<r>/(2*pi)~20 pixels/time increment, where w0 is the radian driving frequency, <r> is the mean separation between particles The learner may find that certain combinations of the selectable parameters do not result in a stable solid. If that is the case, a restart can be accomplished by hitting the F5 key for Windows or the equivalent key for any other operating system. VLJ bExp amp w0 psiV nRows nCols Longitudinal Wave Transverse Wave