  We study a system composed by a three-level giant atom (3GA), a waveguide
initially in the vacuum state, and a single-mode cavity. The 3GA-cavity system
is in a strong-coupling regime, and the distance between the coupling points is
comparable to the coherent length of a spontaneously emitted photon. The
dynamics of the 3GA and its radiative field in the waveguide for long time are
analyzed. Besides the steady value, we also found an oscillatory character of
the excited state population, a signature of oscillating bound states which is
generated by the superposition of two bound states in the continuum. The
radiative field propagates in the cavity-like geometry formed by the coupling
points. When one bound state is emergent, a sine-like interference pattern is
visible for the emitted field intensity in spacetime. An oscillatory character
in time and a beat in space for the emitted field intensity are observed when
two bound states are emergent in a subspace. The wavelengths and the periods
are controlled by the number of the photons in the cavity.
