Discontinuities in the sound speed or its derivatives (or, to be more general, regions where the scale of variation is small compared with the wavelength ), give rise to quasi-periodic variations in the frequencies proportional to , where is the sound travel time from the upper boundary, or the centre, to the source region. Signals from the HeII ionization zone and the lower boundary of a convective envelope can be detected in the difference between the actual frequencies and a smooth fit to an asymptotic expression, or, equivalently, by forming frequency combinations such as (Gough 1990, Roxburgh and Vorontsov 1993b) or . Two periodicities can be seen in Fig. 2.3a where we plot for a solar model; the large-amplitude signal with a period 830Hz and rapidly decreasing amplitude is due to the HeII ionization zone, the smaller-amplitude signal with a period 220Hz is due to the base of the convective zone. In stars with convective cores the difference in composition between the core and envelope that develops during main sequence evolution leads to a very sharp change in density across this interface; this generates a periodic signal in the frequency separations. This can be seen in Fig. 2.3b where we show both the small separation and the separation for a model of a main-sequence star where the hydrogen content in the core has been reduced to 0.5 from an initial value of 0.7.
The amplitude of these signals at a given frequency depends on the nature of the steep changes at . In the helium ionization zone this is due primarily to the change in adiabatic exponent which depends principally on the helium abundance and the equation of state (cf. Vorontsov et al. 1992). If the equation of state is known, then this signal gives an estimate of the helium abundance that is essentially independent of the internal structure of the star. Such an empirical relation between the entropy (or the mixing length) and the surface properties of stars will provide valuable information for modelling the surface regions of other stars, and provide a empirical base for the development of a realistic model of convection. The amplitude of the signal from the base of the convective zone is governed predominantly by the degree of convective penetration (see Roxburgh and Vorontsov 1993b, Gough and Sekii, 1993). The amplitude of the signal from a convective core is governed also by the sharp change in chemical composition, and therefore density, that develops during stellar evolution.