Mathematical models for flows on networks arise in a variety of practical applications, including traffic flow, gas transport in pipelines, supply chain dynamics, and blood circulation. Such systems are typically described by partial differential equations defined on networks, where edges represent one-dimensional flow channels and nodes correspond to junctions. We consider kinetic and related macroscopic equations on networks. In this talk, a class of linear kinetic BGK models is considered, where the limit equation for small Knudsen numbers is given by the wave equation. Coupling conditions for the macroscopic equations are obtained from the kinetic coupling conditions via an asymptotic analysis near the nodes of the network and the consideration of coupled solutions of kinetic half-space problems. Analytical results are obtained for a discrete velocity version of the coupled half-space problems. Moreover, an efficient spectral method is developed to solve the coupled discrete velocity half-space problems. In particular, this allows to determine the relevant coefficients in the coupling conditions for the macroscopic equations from the underlying kinetic network problem. These coefficients correspond to the so-called extrapolation length for kinetic boundary value problems. Numerical results show the accuracy and fast convergence of the approach. Moreover, a comparison of the kinetic solution on the network with the macroscopic solution is presented.