# Where are the harmonics in the radio spectrum?

When I strike a string on my guitar and look at the audio spectrum, I can see the fundamental frequency as a large peak. I can also see the harmonic frequencies as a train of little peaks at increasingly higher frequencies. When I tune an oscillator to produce a pure tone and drive a speaker, predictably I don't see any harmonics.

Do harmonics occur in the radio spectrum reserved for communications?

Radio communications are usually frequency modulated (FM) or amplitude modulated (AM). The fundamental frequency is the "carrier" wave. Frequency modulation induces harmonics, which is this case are a lot more complex than those than a musical instrument. You can produce frequency modulation by taking a signal which is a non linear combination of sine waves, for example $$~\sin(\omega_1 t)\cdot \sin(\omega_2 t)$$ with $$\omega_1\neq\omega_2$$. You can look at the audio spectrum of a signal like this to get a visual intuition.