  Scattering wave systems that are periodically modulated in time offer many
new degrees of freedom to control waves both in spatial and frequency domains.
Such systems, albeit linear, do not conserve frequency and require the
adaptation of the usual theories and methods. In this paper, we provide a
general extension of transmission line or telegraph equations to periodically
time-modulated systems. As a by-product of the theory, we obtain a general
approach to compute and measure the complete scattering matrix of such systems.
Finally, the proposed theory and methods are applied and validated on a
concrete practical example in the realm of airborne acoustics: a time-modulated
actively controlled loudspeaker membrane terminating a monomode waveguide.
Different modulation functions and parameters are tested. The experimental
results are compared to both numerical simulation and an analytical model based
on a two time-scale method.
