With frequency mixers in radios they multiply frequencies to create an intermediate frequency, but where in the wave are those? Every picture I’ve seen makes the two original signals look pretty obvious, but I don’t get where the sum and the difference are.
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When you multiply two sinusoids, the result in general is NOT a sinusoid. It will be obviously repetative and may superficially resemble one sinusoid modulated by the other, but it is not.
It is tough for us to see frequencies in waveforms that are not a pure sinusoid even if they are there.
A square wave contain all odd harmonics of a fundemental sine wave, and yet it looks square. Those other frequencies are there, but your eye cannot see them.
You can run the multiplied signals through a fourrier transform to reveal the presence of the sum and difference frequencies.
Alternatively you can pass the multiplied signal through a bandpass filter at the sum/difference frequency. You should see a nice clean sinusoid.
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