Recent results in quantitative homogenization of the wave equation with rapidly oscillating coefficients are discussed from the operator-theoretic perspective, which views the solution as the result of applying the operator of hyperbolic dynamics, i.e., the unitary group of a self-adjoint operator on a suitable Hilbert space. A prototype one-dimensional example of utilizing the framework of Ryzhov boundary triples is analyzed, where operator-norm resolvent estimates for the problem of classical moderate-contrast homogenization are obtained. By an appropriate “dilation” procedure, these are shown to upgrade to second-order (and more generally, higher order) estimates for the resolvent and the unitary group describing the evolution for the related wave equation.