  We identify a characteristic pattern in the scalar-induced stochastic
gravitational wave background from particle production during inflation. If
particle production is sufficiently efficient, the scalar power spectrum
exhibits $\mathcal{O}(1)$ oscillations periodic in $k$, characteristic of a
sharp feature, with an exponentially enhanced envelope. We systematically study
the properties of the induced spectrum of gravitational waves sourced after
inflation and find that this inherits the periodic structure in $k$, resulting
in a peak in the gravitational wave energy density spectrum with
$\mathcal{O}(10 \%)$ modulations. The frequency of the oscillation in the
scalar power spectrum is determined by the scale of the feature during
inflation and in turn sets the frequency of modulations in the gravitational
wave signal. We present an explicit realisation of this phenomenon in the
framework of multifield inflation, in the form of a strong sharp turn in the
inflationary trajectory. The resulting stochastic background is potentially
detectable in future gravitational wave observatories, and considerations of
backreaction and perturbativity can be used to constrain the parameter space
from the theoretical side. Our work motivates more extensive research linking
primordial features to observable properties of the stochastic background of
gravitational waves, and dedicated development in data analysis for their
detection.
