Speed of sound in a mass–spring chain

N springs of stiffness k connect masses m, spaced 1 unit apart. The left end is a piston whose motion is prescribed. A disturbance travels along the chain at : stiffness over inertia.

Control panel
Chain
Piston
Display
Theory
Piston at the left starts from rest and moves at constant speed w for time t. A front runs ahead at the unknown speed c. Ahead of the front everything is undisturbed; behind it everything moves at w. chain, spacing 1, mass per blob fluid, cross-section front has reached piston has moved mass set in motion its length now mass per length, before → after strain: change in length over original length force on the piston momentum of the moving part speed of propagation
Theory – analogies
stiffnessinertiavalue
mass on a spring
chain, spacing a
solid rodsteel 5 000 m/s
liquidwater 1 500 m/s
gasair 340 m/s
string, tension T per length
shallow water, depth h1 m deep: 3 m/s
pendulum, length L
LC circuit