How are travelling waves reflected at boundaries?

Travelling waves are reflected at boundaries by changing their direction and potentially their speed and amplitude.

When a travelling wave encounters a boundary, such as the end of a string or a change in medium, it cannot simply disappear. Instead, it undergoes a process known as reflection. This is a fundamental concept in wave physics, and it's crucial to understanding phenomena such as echoes, optical reflections, and even the behaviour of electromagnetic waves.

The reflection of a wave at a boundary depends on the properties of the wave and the boundary. If the boundary is fixed, the wave will be reflected back along the path it came from, but it will be inverted. This means that peaks become troughs and vice versa. This is because the fixed boundary cannot move, so the wave is forced to 'flip over' in order to continue its motion.

If the boundary is free or less rigid, the wave will still be reflected, but it will not be inverted. This is because the boundary can move, allowing the wave to continue its motion without needing to flip over. The speed and wavelength of the wave will remain the same, but the amplitude may change depending on the properties of the boundary.

In some cases, a wave can be partially reflected and partially transmitted at a boundary. This is known as partial reflection and transmission. The proportions of the wave that are reflected and transmitted depend on the impedance mismatch between the two media. If the impedance of the second medium is higher, more of the wave will be reflected and less will be transmitted. Conversely, if the impedance of the second medium is lower, more of the wave will be transmitted and less will be reflected.

In summary, the reflection of travelling waves at boundaries is a complex process that depends on the properties of the wave and the boundary. It involves changes in direction, and potentially speed and amplitude, and can result in both reflection and transmission of the wave.