Inside narrow pores, for instance, realized as carbon nanotubes, water forms structures that strongly differ from the structure of bulk liquid water or ice. Here we compute vibrational spectra of such systems using molecular dynamics simulation combined with quantum mechanical perturbation theory. We focus on the spectroscopic response of single-file water chains in pores with subnanometer diameter, finding characteristic signatures of dangling and hydrogen-bonded hydrogen configurations occurring in this particular form of water. These features in the absorption spectra permit us to distinguish single-file water from the stacked-ring structures that form in wider pores. As previously observed in bulk liquid water, the vibrational frequency of the OH stretch of an HDO molecule in a system of D(2)O molecules is essentially determined by the electric field acting at the position of the hydrogen atom, providing a way to link the spectroscopic response to the local charge distribution of specific molecular arrangements.