Describe how a standing wave is formed.

A standing wave is formed when two waves of the same frequency and amplitude interfere constructively and destructively in a medium.

In more detail, standing waves, also known as stationary waves, are the result of the superposition of two waves moving in opposite directions. These waves must have the same frequency, wavelength and amplitude. They are typically formed in a medium that is bounded or fixed at both ends, such as a string on a musical instrument or the air column in a wind instrument.

The formation of a standing wave begins when a wave is introduced into a medium, and it encounters a boundary that reflects it back. This reflected wave then interferes with the incoming wave. If the two waves meet at just the right moment, they will interfere constructively, their amplitudes adding together to create a point of maximum displacement known as an antinode. If they meet at just the wrong moment, they will interfere destructively, cancelling each other out to create a point of zero displacement known as a node.

The pattern of nodes and antinodes is what gives a standing wave its characteristic appearance. Unlike a travelling wave, which moves through a medium, a standing wave appears to stay in one place, with the points of maximum and minimum displacement remaining fixed. This is why it is called a 'standing' or 'stationary' wave.

The frequency at which a standing wave is formed in a medium is determined by the medium's natural frequencies, or harmonics. These are the frequencies at which the medium naturally vibrates. For a string, for example, the fundamental frequency, or first harmonic, is the frequency at which the entire length of the string vibrates as a single segment. The second harmonic, or first overtone, is the frequency at which the string vibrates as two segments, and so on. When a wave is introduced into the medium at one of these frequencies, it will resonate with the medium and form a standing wave.

In summary, the formation of a standing wave is a complex process involving wave reflection, interference, and resonance. It requires precise conditions, but when these are met, the result is a wave that appears to stand still, with a pattern of nodes and antinodes that remains fixed in space.