been scaled by the inertia ratio, $Q_{n,l}$. The errorbars on these figures are not visible because they are smaller than the symbol size. Results obtained using GONG frequencies. []{data-label="figure[shift vs freq]"}](freq_dependence_scaled.jpg "fig:"){width="45.00000%"}\

Dependence of solar cycle frequency shifts on mode inertia
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The main $l$-dependence in $\delta\nu_{n,l}$ is associated with mode inertia. The normalized mode inertia is defined by @1991sia..book..401C as $$\label{equation[mode inertia]}
   I_{n,l}=M_\odot^{-1}\int_{v}|\xi|^2\rho\textrm{d}V=
   4\pi M_{\odot}^{-1}\int_0^{R_s}|\xi|^2\rho r^2\textrm{d}r=
   \frac{M_{n,l}}{M_{\odot}},$$ where $\xi$ is the displacement associated with a mode, suitably normalized at the photosphere, $V$ is the volume of the Sun, and $M_{\odot}$ is the mass of the Sun. $M_{n,l}$ is the ‘mass’ associated with a mode. The physical interpretation of the mode inertia is some measure of the interior mass affected by any given mode. At fixed frequency a decrease in $l$ results in an increase in $M_{n,l}$ and therefore in $I_{n,l}$. In other words as $l$ decreases a greater volume of the interior is associated with the motions generated by the mode. Therefore the high-$l$ modes are more sensitive to a perturbation and so vary more throughout the solar cycle than low-$l$ modes.

The inertia ratio, $Q_{nl}$, is defined by @1991sia..book..401C as: $$Q_{nl} = I_{nl} / \bar{I}(\nu_{nl}),
 \label{eqution[inertia ratio]}$$ $\bar{I}(\nu_{nl})$ 