  Large groups of active cilia collectively beat in a fluid medium as
metachronal waves, essential for some microorganisms motility and for flow
generation in mucociliary clearance. Several models can predict the emergence
of metachronal waves, but what controls the properties of metachronal waves is
still unclear. Here, we investigate numerically a simple model for cilia in the
presence of noise on regular lattices in one- and two-dimensions. We
characterize the wave using spatial correlation and the frequency of collective
beating. Our results clearly show that the viscosity of the fluid medium does
not affect the wavelength; the activity of the cilia does. These numerical
results are supported by a dimensional analysis, which is expected to be robust
against the model for active force generation, unless surrounding fluid
influences the cilia activity. Interestingly, enhancement of cilia activity
increases the wavelength and decreases the beating frequency, keeping the wave
velocity almost unchanged. These results might have significance in
understanding paramecium locomotion and mucociliary clearance diseases.
