Explain the Natural Frequencies and Resonance

Standing waves occur when the waves, like those in a vibrating piece of rope, are repeating so that there are places on the rope that stay still, called nodes. If you can see no points that stay still, the wave is moving or propagating. The antinodes are halfway between the nodes in a standing wave, and are the points of maximum amplitude.

If I have a piece of rope of length l, attached to the back of a chair, this rope will want to wiggle with natural frequencies to produce standing waves. The length of the rope will be a multiple of a wavelength of the motion, so that an even number of wavelengths will fit on the rope. The lowest natural frequency causes vibrations, where the length of the rope is equal to its wavelength (the bottom example of the three above).

The natural frequencies of an object are controlled by the object's size and the springiness of the material the object is made of. If I drop a billiard ball and a ping-pong ball, they make very different sounds. The sound waves generated by dropping them have different natural frequencies. The ping-pong ball makes a higher frequency sound (more vibrations per second - higher pitch) while the billiard ball makes a lower frequency sound (fewer vibrations per second - lower pitch). We also call a low-frequency sound a low-pitch sound; we call a higher frequency sound a sound with higher pitch. The natural frequency produces standing waves in the object and requires minimum energy to produce forced vibrations.

Resonance happens when a force is applied at the natural frequency of the system. Suppose you are pushing your younger sister on a swing. If you push her forward with the same force each time, always at the moment that she swings furthest back, you will make her swing higher and higher until you stop pushing. Resonance means that the same force can produce larger and larger vibrations, because the applied frequency is the same as the natural frequency.