Notice again that neither the carrier frequency nor the modulation frequency are present in the spectrum.
Because of its spectrum, RM is also sometimes called double-sideband (DSB) modulation.
Ring modulating can be realized without oscillators just by multiplying two signals together.
The multiplication of two complex sounds produces a spectrum containing frequencies that are the sum and difference between each of the frequencies present in each of the sounds.
The number of components in RM is two times the number of frequency components in one signal multiplied by the number of frequency components in the other.