  Asteroseismology has been used extensively in recent years to study the
interior structure and physical processes of main sequence stars. We consider
prospects for using pressure modes (p-modes) near the frequency of maximum
oscillation power to probe the structure of the near-core layers of main
sequence stars with convective cores by constructing stellar model tracks.
Within our mass range of interest, the inner turning point of p modes as
determined by the JWKB approximation evolves in two distinct phases during the
main sequence, implying a sudden loss of near-core sensitivity during the
discontinuous transition between the two phases. However, we also employ
non-JWKB asymptotic analysis to derive a contrasting set of expressions for the
effects that these structural properties will have on the mode frequencies,
which do not encode any such transition. We show analytically that a
sufficiently near-core perturbation to the stellar structure results in
non-oscillatory, degree-dependent perturbations to the star's oscillation mode
frequencies, contrasting with the case of an outer glitch. We also demonstrate
numerically that these near-core acoustic glitches exhibit strong angular
degree dependence, even at low degree, agreeing with the non-JWKB analysis,
rather than the degree-independent oscillations which emerge from JWKB
analyses. These properties have important implications for using p-modes to
study near-core mixing processes for intermediate-mass stars on the main
sequence, as well as for the interpretation of near-center acoustic glitches in
other astrophysical configurations, such as red giants.
