Three-minute oscillations are observed in the chromosphere above sunspot umbrae. One of the models used to explain these oscillations is that of a chromospheric acoustic resonator, where the cavity between the photosphere and transition region partially reflects slow magnetoacoustic waves to form resonances in the lower sunspot atmosphere. We present a phenomenological study that compares simulation results with observations. The ideal magnetohydrodynamic equations are used with a uniform

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... al magnetic field and a temperature profile that models sunspot atmospheres above umbrae. The simulations are initialised with a single broadband pulse in the vertical velocity, inside the convection zone underneath the photosphere. The frequencies in the spectrum of the broadband pulse that lie below the acoustic cutoff frequency are filtered out so that frequencies