# Can sound with lower frecuency without overtones produce standing wave of higher frequency?

I read that resonance appears if frequencies are equal. What if vocal cord produce only pure tone without harmonics, will voice still have overtones? Or will sound of guitar with only one string which produce only pure tone without harmonics still have overtones? Added question: Can sound(without overtones) of frequency for example 220 Hz produce standing waves in cavity with natural frequency 440 Hz For example Helmholtz resonator reacts only on its own frequency of sound, but is there shape of cavity which react to lower frequency? One more example pendulum with natural frequency 8 Hz can react to frequency 2 Hz or 4 Hz.

• By definition, if a sound only contains one pure tone it does not have overtones. But it is very difficult to produce a "pure tone" since humans can detect sounds (without hearing damage) with a pressure amplitude range of about 1 million to 1. Vocal chords and guitar strings, do not produce anything close to "pure tones" in real life. Commented Feb 9, 2019 at 19:34
• But can sound of frequency for example 220 Hz produce standing waves in cavity with main frequency 440 Hz? Commented Feb 9, 2019 at 20:09
• As alephzero stated, asking for harmonics (or overtones in general even if they are not harmonically related) related to a pure (co)sinusoidal excitation is against its own definition. A pure (co)sinusoidal signal contains a single frequency by definition so it cannot have overtones. Regarding the resonance, the answer is no. You can check in simple tubes/pipes and strings to see that if the frequency is not supported by the system (it is not one of its natural frequencies) the boundary conditions are not satisfied and thus the frequency does not "resonate". Commented May 14, 2023 at 19:23