What are standing waves and how are they formed?

Standing waves are wave patterns that appear to stay in one place, formed by the interference of two waves travelling in opposite directions.

In more detail, standing waves, also known as stationary waves, are a result of the superposition of two waves of the same frequency and amplitude, moving in opposite directions. This phenomenon is often observed in musical instruments, such as a guitar string or a wind instrument, where the waves are reflected back and forth.

When these two waves meet, they interfere with each other. If they meet in such a way that their peaks and troughs align, they will constructively interfere, creating areas of maximum displacement known as antinodes. If they meet in such a way that a peak of one wave aligns with a trough of the other, they will destructively interfere, creating areas of zero displacement known as nodes. The pattern of nodes and antinodes thus created gives the appearance of a wave standing still, hence the name 'standing wave'.

The formation of standing waves is not limited to musical instruments. They can also be observed in other physical phenomena such as electromagnetic waves inside a microwave oven, or even in quantum physics where the wave-like nature of particles can lead to standing wave patterns.

The key to understanding standing waves is the principle of superposition, which states that when two or more waves meet, the resultant displacement at any point is the vector sum of the displacements that the individual waves would cause at that point. This principle is fundamental to wave behaviour and is the reason why standing waves appear to stay in one place, despite being the result of two waves travelling in opposite directions.