  We study the Faraday patterns generated by spin-orbit-coupling induced
parametric resonance in a spinor Bose-Einstein condensate with repulsive
interaction. The collective elementary excitations of the Bose-Einstein
condensate, including density waves and spin waves, are coupled as the result
of the Raman-induced spin-orbit coupling and a quench of the relative phase of
two Raman lasers without the modulation of any of the system's parameters. We
observed several higher parametric resonance tongues at integer multiples of
the driving frequency and investigated the interplay between Faraday
instabilities and modulation instabilities when we quench the
spin-orbit-coupled Bose-Einstein condensate from zero-momentum phase to
plane-wave phase. If the detuning is equal to zero, the wave number of
combination resonance barely changes as the strength of spin-orbit coupling
increases. If the detuning is not equal to zero after a quench, a single
combination resonance tongue will split into two parts.
