波浪的反射

When a propagating wave encounters the boundary of any medium, it gets reflected. The wave traveling from the source toward the boundary is called the incident wave, while the wave bouncing back is the reflected wave. The behavior of the reflected wave depends on whether the boundary is fixed or free to move.

At a fixed boundary, the reflected wave is 180° out of phase with the incident wave, causing inversion. According to Newton's third law, as the incident wave exerts an upward force on the fixed boundary, the boundary exerts an equal and opposite downward force on the wave. This force reversal causes a crest to become a trough and vice versa, though amplitude remains unchanged.

At a free boundary, the reflected wave maintains the same amplitude and phase as the incident wave with no inversion. The boundary can move freely with the wave's oscillations, so if the incident wave is a crest, the reflected wave is also a crest. This contrasts with fixed boundaries, where the reflected wave inverts 180°.

When a string is tied to a solid ring capable of sliding along a frictionless pole, the end acts as a free boundary. The ring moves up and down with the wave's oscillations, traveling to maximum height equal to the wave's amplitude. The reflected wave maintains the same phase as the incident wave, so a trough remains a trough after reflection.

A fixed boundary condition occurs when the boundary of a medium cannot move with the wave's oscillations, such as a string tied to a wall. The boundary is immovable, forcing the incident wave to reflect with a 180° phase shift. The amplitude of the reflected wave remains unchanged assuming no energy losses occur.

Sound waves reflecting off a cliff create an echo, demonstrating wave reflection. When you yell toward a cliff, longitudinal sound waves travel through air and reflect from the cliff's boundary. Similarly, flipping one end of a string tied to a wall sends a transverse wave pulse through the string that reflects upon reaching the wall.

When a wave reflects at either a fixed or free boundary, the amplitude of the reflected wave remains equal to the incident wave's amplitude, assuming no energy losses. The phase may change 180° at fixed boundaries or remain unchanged at free boundaries, but the magnitude of oscillation stays constant. This principle applies to interference and superposition of waves.