Show and explain the vertical displacement of a particle, a distance from the origin for a wave travelling from negative direction.
To determine the vertical displacement of a particle in a wave traveling from the negative direction, we need to understand a few concepts related to waves.
First, let's define what we mean by "vertical displacement." In a wave, vertical displacement refers to how far a particle has moved above or below its equilibrium position as it oscillates. The equilibrium position is the point where the particle would rest if there were no wave passing through it.
Next, we need to understand that a wave is a disturbance that propagates through a medium. It can be described by various parameters, including amplitude, wavelength, frequency, and speed.
When a wave is traveling from the negative direction, it means that the wave is moving in the opposite direction of a positive coordinate axis. This is often represented as a wave moving from right to left on a graph.
Now, let's consider a specific example to illustrate the vertical displacement of a particle in a wave traveling from the negative direction. Suppose we have a transverse wave traveling from the left to the right along a string.
In this scenario, the particles of the string will move up and down as the wave passes through them. Let's say we select a specific particle and track its motion.
As the wave approaches the particle from the negative direction, the particle will initially be at its equilibrium position. As time progresses, the wave will cause the particle to move above and below its equilibrium position. The maximum displacement above the equilibrium position is the amplitude of the wave, while the maximum displacement below the equilibrium position is the negative amplitude of the wave.
Therefore, the vertical displacement of a particle at any given time can be determined by measuring its distance from the equilibrium position. If the particle is above the equilibrium position, the displacement will be positive, while if the particle is below the equilibrium position, the displacement will be negative.
To summarize, the vertical displacement of a particle in a wave traveling from the negative direction refers to the distance it has moved above or below its equilibrium position as the wave passes through it. By measuring this distance from the equilibrium position, we can determine the particle's displacement at any given time.