To describe a traveling wave in English, Thai, or Japanese five things must be defined. The shape, the amplitude, the wavelength, the speed and the direction of travel. If spoken language was used the description would be long and not 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 efficient to describe a wave with a mathematical equation. That way other people know exactly what is meant and the explanation is short. The wave can immediately be displayed on a calculator and everyone can see what it looks like.
The most common wave shape is described as ....
y = A sin(x)
To change the wavelength the value of the constant in front of the x is changed.
If the wavelength is two units the equation becomes ....
y = A sin 3.14(x)
To make the wavelength a constant l [the Greek letter lambda] the equation has 2p over l in front of the x.
The equation becomes ...
y = A sin(2p/l)x
Replacing the x by (x - 0.5) moves the sine wave to the right by one half space.
The equation becomes ...
y = A sin p (x - 0.5)
0.5 is called the phase constant. A phase constant shifts the origin. If the phase constant increases with time the wave moves to the right or the left depending on the sign in the bracket. A plus sign to the left and a negative sign to the right.
The equation of a sine wave traveling to the right with speed v is....
The equation of a sine wave traveling to the left with speed v is....
> Quiz