Turns out, adding in the frequency domain looks like multiplication in the time domain, so we actually want to multiply the two signals together. In general, a good math model for a sine wave is: ...

According to the Fourier theorem, periodic sound may be shown to consist of sine waves in the harmonic series ... A more general form of analysis for transferring a time-domain signal to the frequency ...

I remember coming to the understanding that a square wave, which is a collection of fundamental and (odd) harmonics frequencies, could then be used to give an indication of frequency response.