When two waves travel together along the same line, it is represented by a phenomenon called superposition. Superposition occurs when two or more waves combine or overlap with each other, resulting in a new wave pattern.
The principle of superposition states that the displacement (or any other measurable quantity) of the combined wave at any given point is the algebraic sum of the displacements of the individual waves at that point. In other words, the waves add up to create a resultant wave.
If the two waves have the same frequency, wavelength, and amplitude, and they are in phase (their crests and troughs align), they can constructively interfere. This means that their displacements add up, resulting in a wave with a larger amplitude.
If the two waves have the same frequency, wavelength, and amplitude, but they are out of phase (their crests and troughs do not align), they can destructively interfere. This means that their displacements partially or completely cancel each other out, resulting in a wave with a reduced or zero amplitude at certain points.
The mathematical representation of superposition involves adding the individual wave equations to obtain the equation for the resultant wave. The resulting wave can exhibit complex patterns depending on the phase relationship and the properties of the individual waves.
Overall, the phenomenon of superposition allows waves to combine and interact with each other, leading to a rich variety of wave behaviors and patterns.