  In this note we prove that the asymptotic variance of the nodal length of
complex-valued monochromatic random waves restricted to an increasing domain in
$\R^3$ is linear in the volume of the domain. Put together with previous
results this shows that a Central Limit Theorem holds true for $3$-dimensional
monochromatic random waves. We compare with the variance of the nodal length of
the real-valued $2$-dimensional monochromatic random waves where a faster
divergence rate is observed, this fact is connected with Berry's cancellation
phenomenon. Moreover, we show that a concentration phenomenon takes place.
