Exercise 4

Dominoes falling make a wave. We may conjecture that the wave speed $v$ depends on the spacing $d$ between the dominoes, the height $h$ of each domino, and the acceleration due to gravity $g$.

• Find the dimensional formula for each of the four quantities.

• Show that $\{\hskip 1.00006pt\Pi_{1}=h/d,\Pi_{2}=dg/v^{2}\hskip 1.00006pt\}$ is a complete set of dimensionless products.

• Show that if $h/d$ is fixed then the propagation speed is proportional to the square root of $d$.