**The Wave Equation**

In deriving the motion of a string under tension we came up with an equation:

**Waves Add**

Say you have two waves governed by two equations Since they are traveling in
the same medium,

Lets say we have two functions,

**General Form**

Any well behaved (ie. no discontinuities, differentiable) function of the form

Lets take the example of a Gaussian pulse.

Then

and

**The velocity of a Wave**

To find the velocity of a wave, consider the wave:

#### Note:

Another way to picture this is to consider a one dimensional wave pulse of
arbitrary shape, described by

#### Note:

**Wavelength, Wavenumber etc.**

We will often use a sinusoidal form for the wave. However we can't use

Also note that the frequency is

**Normal Modes on a String as an Example of Wave Addition**

Lets go back to our solution for normal modes on a string:

Comments:"This book covers second year Physics at Rice University."