The lengths of the pendulums are set such that in a given time t, the first pendulum completes n oscillations, and each subsequent one completes one more oscillation than the previous. As all pendulums are started together, their relative phases change continuously, but after time t, they come back in sync and the sequence repeats.^[1]

For small perturbations, the period of a pendulum is given by

${\displaystyle T=2\pi {\sqrt {\frac {L}{g}}}}$

where L is the length of the pendulum and g is the standard acceleration due to gravity.^[6]

As t/n is the period of a pendulum completing n oscillations in t,

${\displaystyle {\begin{aligned}{\frac {t}{n}}&=2\pi {\sqrt {\frac {L}{g}}}\\\therefore L&=g{\Big (}{\frac {t}{2\pi n}}{\Big )}^{2}\\\end{aligned}}}$

A common choice of t is 60 seconds. Thus, for g ≈ 9.8 ms⁻²,

${\displaystyle L\approx {\frac {894}{n^{2}}}\;{\text{m}}}$

Parameters of the
pendulum wave in
the animation above