  We are concerned with the field concentration between two nearly-touching
inclusions with high-contrast material parameters, which is a central topic in
the theory of composite materials. The degree of concentration is characterised
by the blowup rate of the gradient of the underlying field. In this paper, we
derive optimal gradient estimates for the wave filed of the 3-D Helmholtz
system in the quasi-static regime. There are two salient features of our
results that are new to the literature. First, we cover all the possible
scenarios that the size of the inclusions are in different scales in terms of
the asymptotic distance parameter $\epsilon$, which can be used to characterise
the curvature effects of the shape of the inclusions on the field
concentration. Second, our estimates can not only recover the known results in
the literature for the static case, but can also reveal the interesting
frequency effect on the field concentration. In fact, a novel phenomena is
shown that even if the static part vanishes, field blowup can still occur due
to the (low) frequency effect.
