We could describe a traveling wave in English, Thai or Japanese. To do that properly and completely we would need to define the shape, the amplitude, the wavelength, the speed and the direction of travel. The description would be long and not very easy to understand. The person listening would get some idea of what the wave looked like but would not get it exactly.
It is more exact and more efficient to describe a wave with a mathematical equation. That way other people know exactly what we mean and the explanation is short. That way we can type the equation in to Graphing Calculator and see exactly what the wave looks like.
To change the wavelength we change the value of the constant in front of the x.
To make the wavelength a constant l [the Greek letter lambda] the equation has 2p over l in front of the x.
Replacing the x by (x - 0.5) moves the sine wave to the right by one half space.
The new constant inside the bracket is called a phase constant. A phase constant shifts the origin. In other words, the graph no longer starts at the origin.