We analyse the post-inflationary contribution to the stochastic gravitational wave background due to a resonant feature in the scalar power spectrum, which is characterised by an oscillation in $log(k)$, complementing our previous work arXiv:2012.02761 on sharp features. Primordial features signal departures of inflation from the single-field slow-roll paradigm and are motivated by embeddings of inflation in high energy physics. We find that the oscillation in the scalar power spectrum leads to a corresponding modulation in the gravitational wave spectrum that can be understood as a superposition of two oscillatory pieces, one with the original frequency of the scalar oscillations, and one with double frequency. For oscillations with slowly-varying amplitude this oscillatory part can be computed semi-analytically. Our results can be used as templates for the reconstruction of the signal from future data and permit extracting information about the small scale scalar power spectrum from measurements of the stochastic gravitational wave background.
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