  We seek to address whether solar-cycle frequency shifts of the Sun's low-l p
modes `distort' the underlying shapes of the mode peaks, when those peaks are
observed in power frequency spectra made from data spanning large fractions, or
more, of the cycle period. We present analytical descriptions of the expected
profiles, and validate the predictions through use of artificial seismic
timeseries data, in which temporal variations of the oscillator frequencies are
introduced. Our main finding is that for the Sun-like frequency shifts the
distortion of the asymmetrical Lorentzian-like profiles is very small, but also
just detectible. Our analysis indicates that by fitting modes to the usual
Lorentzian-like models -- which do not allow for the distortion -- rather than
new models we derive, there is a bias in the mode height and linewidth
parameters that is comparable in size to the observational uncertainties given
by multi-year datasets. Bias in the frequency parameter gives much less cause
for worry, being over an order of magnitude smaller than the corresponding
frequency uncertainties. The distortion discussed in this paper may need to be
considered when multi-year Sun-like asteroseismic datasets are analyzed on
stars showing strong activity cycles.
