In an unloaded chain of elastic spheres, Hertz contact makes the medium a sonic vacuum, so an impact travels as a solitary wave rather than sound. When the striker is heavier than a bead, repeated secondary collisions split the impulse into a train of solitary waves whose peak forces fall off exponentially with pulse number. Students learn how treating each solitary wave as a quasi-particle with an effective mass of about 1.345 bead masses, plus energy and momentum conservation, yields a closed-form decay coefficient that depends only on the striker-to-bead mass ratio and not on impact strength -- the basis for tuning granular layers for shock and blast mitigation.
A chain of identical elastic spheres that barely touch cannot carry ordinary sound: because Hertz contact makes the repulsive force grow as the 3/2 power of the overlap, an unloaded chain is a 'sonic…