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Physical Representations explain the features of the situation in a visual way, often with vector representations of physical quantities overlaid a simple diagram or picture of the situation.

When two waves with equal frequency and magnitude travel in opposite directions they create standing waves. Below is a figure with several snapshots with a green wave traveling left and a blue wave traveling to the right, where the red line is the sum of the two traveling waves. As the waves propogate they add in a such a way to produce a standing wave.

Mathematical Representation uses equation(s) to describe the situation.

 

Symetric boundary conditions,

$\lambda_m = \frac{2L}{m},   m = 1,2,3,4,5,...$

Antisymetric boundary conditions,

$\lambda_m = \frac{4L}{m},   m = 1,3,5,7,9,...$

$f_{m} = \frac{\nu}{\lambda_{m}}$

Wavelength ($\lambda$), Velocity ($\nu$), Integer ($m$)

Graphical Representation describes the situation through use of plots and graphs.

Symetric boundary conditions.

Antisymetric boundary conditions

Descriptive Representation is made up entirely of words or annotations. Think about how you might explain the situation to someone else.

 

Standing waves are created by waves with the same frequency, wavelength, and ideally amplitude which are traveling in opposite directions. They add in such a way that it looks like the wave is just occilating up and down. However, the waves are still moving back and forth, but the contructive and destuctive interference of the two waves occur at fixed positions relative to the geometry of the system.

Experimental Representation could be thought of as doing the experiment.

 

Attach a rope so that one end is fixed, or have two people at each end of a rope. Now, move you hand up and down and find the correct frequency oscillation of your hand to create a standing wave. In the following video observe the motion of the persons hand as he creates several resonant standing waves. The first 2 minutes is important, otherwise please ignore the commentary as they use terminology that is not recommended.