$$\require{cancel}$$
Resonance is a key concept in the production of sound in instruments and in acoustics. We will come across it many more times in this book. The natural frequency ($$f_{o}$$ measured in hertz) is the frequency at which an oscillating system naturally wants to vibrate. For a mass on a spring, this is determined by the size of the mass and the stiffness of the spring; a stiffer spring has a higher natural frequency as we saw in the previous chapter. To keep a system vibrating in the presence of friction we have to keep pushing it with a periodic force. The frequency of this periodic driving force is called the driving frequency, $$f$$ which is totally independent of the natural frequency (we can push our mass on a spring at a frequency different from the frequency at which it wants to vibrate).