In the context of wave motion, the wavelength represents the distance between two successive crests or troughs of the wave. It is a measure of the spatial extent of the wave pattern. Therefore, the wavelength does not represent the distance in the horizontal direction but rather the distance along the direction of wave propagation.
If you are graphing the wave motion of a single medium particle, the horizontal distance does not directly correspond to the wavelength. Instead, it represents the displacement of the particle from its equilibrium position as a function of time. The amplitude, on the other hand, represents the maximum displacement of the particle from its equilibrium position.
To visualize the wave motion graphically, you typically plot the displacement of the particle along the vertical axis (y-axis) and time along the horizontal axis (x-axis). The wave pattern will show the oscillations of the particle as the wave passes through it. The wavelength can be determined by measuring the distance between two corresponding points on the graph, such as two successive crests or troughs.
It's important to note that the amplitude and wavelength are distinct properties of a wave. The amplitude represents the maximum displacement from equilibrium, while the wavelength represents the spatial extent of the wave pattern. The horizontal distance on the graph may not directly correspond to the wavelength but rather represents the passage of time or the position of the particle along the wave's path.