), amplitude (A), velocity (C or V), and frequency (f).wave motion is defined as the movement of a distortion of a material or medium, where the individual parts or elements of the material only move back-and-forth, up-and-down, or in a cyclical pattern.
Characteristics of waves: wavelength (), amplitude (A), velocity (C or V), and frequency (f).
):the distance from one crest (or maximum of the wave) to the next crest or maximum.
Waveform showing wavelength and amplitude
The height of the wave is called its amplitude. Some areas consider the middle of the wave to its peak as the amplitude, while others consider peak-to-peak as the amplitude.
The velocity of the wave is the measurement of how fast a crest is moving from a fixed point. For example, the velocity of water waves can be measured as their speed in a given direction with respect to the land.
The frequency of waves is the rate the crests or peaks pass a given point. Frequency is the wavelength divided by the velocity and is designated as cycles (or peaks) per second. Cycles per second is also called Hertz.
Frequency = Velocity / Wavelength
Another way of writing that is:
Here's a wave moving to the right. (Applying the notion scaling and shifting in the wave motions) If the wave shape at time zero has the form y=f(x), then a moving wave will have a shape at later time y=f(x-Vt).
It's the same f, so it's the same shape, just located at a shifted value of x. Left moving waves will have the shape y=f(x+Vt). Any point on the wave travels at (x-Vt=constant), i.e. with velocity V. This is called the "phase velocity", because if you think of f as a sin wave, then this is the velocity that any given phase (like e.g., Pi/2, the peak) moves.
So the simplest form of a wave in 1D is the "harmonic wave",i.e. sinusoidal:
The travelling wave is then
(A is the amplitude.)
We can also use cosine instead of sin (this is the SAME function, just phase shifted).