  This note deals with nodal domains of random monochromatic plane waves. It
was shown by Nazarov and Sodin that the expected number of such nodal domains
included in a disk of radius $R$ is proportional to $\pi R^2$ in the large $R$
limit. However, very little is known on the value of the proportionality
constant from a mathematical point of view. The aim of this note is to obtain a
lower bound on the value of this constant my elementary means.
