ELI5: Why plucking a string harder on (for example) a guitar doesn't increase its pitch (see text).

I'm not an expert and people should feel free to correct me, but I think pendulum analogy is misleading.

After you pluck the string, the string does not vibrate due to its momentum like a pendulum, because it's not free to do so, due to the tension. Instead, any disturbance is immediately carried away along the string, at a constant speed. This speed depends on the tension and the density of the string, not how hard you plucked the string (I can't tell exactly why but it's similar to the speed of sound being constant in air). Then, the disturbance is reflected at the bridge or frets, and returns to the point where the it was originated, and this process repeats. Since the speed is constant, the duration of this repetition depends on the length of the string, and this repetition is what creates the vibration and the duration determines the frequency (or pitch, same thing).

/r/explainlikeimfive Thread