  Parametrically-excited surface waves, forced by a periodic sequence of
delta-function impulses, are considered within the framework of the
Zhang-Vi\~nals model (J. Fluid Mech. 1997). The exact impulsive-forcing
results, in the linear and weakly nonlinear regimes, are compared with
numerical results for sinusoidal and multifrequency forcing. We find
surprisingly good agreement between impulsive forcing results and those
obtained using a two-term truncated Fourier series representation of the
impulsive forcing function. As noted previously by Bechhoefer and Johnson (Am.
J. Phys. 1996), in the case of two equally-spaced impulses per period there are
only subharmonic modes of instability. The familiar situation of alternating
subharmonic and harmonic resonance tongues emerges for unequally-spaced
impulses. We extend the linear analysis for two impulses per period to the
weakly nonlinear regime for one-dimensional waves. Specifically, we derive an
analytic expression for the cubic Landau coefficient in the bifurcation
equation as a function of the dimensionless fluid parameters and spacing
between the two impulses. As the capillary parameter is varied, one finds a
parameter region of wave amplitude suppression, which is due to a familiar 1:2
spatio-temporal resonance between the subharmonic mode of instability and a
damped harmonic mode. This resonance occurs for impulsive forcing even when
harmonic resonance tongues are absent from the neutral stability curve. The
strength of this resonance feature can be tuned by varying the spacing between
the impulses. This finding is interpreted in terms of a recent symmetry-based
analysis of multifrequency forced Faraday waves by Porter, Topaz and Silber
(Phys. Rev. Lett. 2004, Phys. Rev. E 2004).
