The acoustic resonator is an important model to explain the three-minute oscillations above sunspot umbrae. The steep temperature temperature gradients at the photosphere and transition region provide the cavity for the resonator, which allows waves to be both partially transmitted and partially reflected. It is found that by analysing the velocity spectra present in the corona, one can estimate the depth of the chromospheric cavity. The magnetic field above umbrae is modelled numerically in 1.5D with slow-magnetoacoustic wave trains travelling along magnetic fieldlines. Resonances are driven by applying continuous random noise as small velocity perturbations to the upper convection zone. Energy escapes the resonating cavity and produces upwards propagating wave trains moving into the corona. The depth of the chromospheric cavity is varied and the resultant coronal velocity spectra are analysed. The results show that the gradient of the coronal velocity spectra is directly correlated with the chromospheric temperature configuration; as the chromospheric depth increases, the spectral gradient becomes shallower. When line of sight integration is performed, the resultant frequency spectra demonstrate a bandwidth containing excited frequencies which becomes narrower as the chromospheric depth increases. These two results provide potentially useful diagnostics for the chromospheric temperature profile by consideration of the coronal velocity oscillations.