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Description
Acoustic waves below the cut-off frequency reflect at the photosphere, forming standing p-modes in sub-photospheric cavities. Above the cut-off, waves propagate as pseudomodes. Recent observations show pseudomode frequencies vary in anti-phase with the 11-year solar cycle, which is not yet fully explained. Using the Klein-Gordon equation with a piecewise acoustic potential, we study the frequency stability of trapped p-modes and propagating pseudomodes, influenced by the acoustic cut-off and wave source location. P-mode frequencies decrease due to the cut-off effect but are insensitive to source depth. Linking the cut-off to the plasma β parameter, we show that solar cycle modulation of the photospheric magnetic field can explain observed p-mode frequency shifts. Pseudomode frequencies, however, depend on both the cut-off effect and source depth. Our model qualitatively reproduces the observed anti-phase variation of pseudomode frequencies with the solar cycle.