mode with a frequency of $\sim1800\,\rm\mu
Hz$ is about $0.996R_\odot$ (approximately 3Mm) below the surface. Note that the upper turning point predicted by a model is strongly dependent on the properties of the model at the top of the convection zone.

![Acoustic cut-off frequency as a function of solar radius. The upper turning point of the modes can be thought of in terms of the acoustic cut-off frequency because the upper turning point corresponds to the radius at which the acoustic cut-off frequency equals the mode frequency. The blue curve shows the cut-off frequencies determined from a standard solar model, while the red curve shows the acoustic cut-off frequency in an isothermal limit. Adapted from @2012ApJ...758...43B.[]{data-label="figure[upper turning points]"}](upper.jpg "fig:"){width="45.00000%"}\

Above $3700\,\rm\mu Hz$ the relationship between frequency shift and activity changes, as the magnitude of the solar cycle frequency shift decreases and oscillates [e.g. @1990Natur.345..779L; @1991ApJ...370..752G; @1996ApJ...456..399J]. Furthermore, above $\sim4100\,\rm\mu Hz$ it appears that modes experience a decrease in frequency as activity increases [@1994SoPh..150..389R; @1998MNRAS.300.1077C].

As we have seen the frequency dependence of the frequency shifts implies that the shifts can be associated with a near-surface perturbation. Therefore, we now move on to directly compare the change in mode frequency with 