## Mathematics 309 - Wave Motion in 1D

### Terms and Concepts

 A = Amplitude ג = Wavelength C = Velocity T = Period ω = Frequency A = The maximum distance from the rest position (0). ג = The spatial distance between two crests of the wave. C = The velocity at which crests travel. T = The time require for one compete up/down cycles or the time to complete one wavelength. ω = The number of cycles per second or radians per second.

### Fundamental Wave Equations

T = 1 / ω (cycles)
= 1 / ( ω / 2∏ ) (radians)

C = Distance/ Time
= ג / T
= ω / ג
= ג ω / 2∏

This equation holds in any number of dimensions if C = speed as opposed to velocity, which has direction.

For example :
|C| = |ג| ω / 2∏    holds in any number of dimension.

### Displacement of Wave

At time 0:
Y = Cos (X)

At time t:
The graph is shifted to the right by the amount ct.
According to the basic idea of shifting and scaling, the new function is

Y = Cost (X - Ct)

We are going to scale 2∏ ---> ג .
Scaling by ג / 2∏.
The new function is Y = Cos (X / (ג /2∏ ))
= Cos ( 2∏X/ג )