Understanding the definition of standing wave

[needingtoknow]

Homework Statement

For standing wave, I have read that there are certain points on the wave that don't move at all, nodes. However, for a standing wave the shouldn't the resultant wave have no displacement because we now have two waves on the same rope with the same amplitude and frequency and according to the interference of waves we should add the amplitude of each wave to get the resultant wave. Since each wave has the same amplitude but in the opposite direction, that means the entire wave should not be moving right? Thanks for your help.

 

[nsaspook]

Watch this:

https://www.youtube.com/watch?v=DovunOxlY1k

 

[needingtoknow]

I saw the part on standing waves but it still doesn't answer why isn't the wave simply a straight line. Why does it still bob up and down?

 

[needingtoknow]

Am I seeing this diagram correctly. Is the solid line the incident wave and the dashed line the reflected wave?

 

[nsaspook]

Am I seeing this diagram correctly. Is the solid line the incident wave and the dashed line the reflected wave?

I assume the diagram is the standing wave that results from the superposition of the forward and reflecting wave movements.

 

[needingtoknow]

Figured it out. The bopping up and down of the standing wave is a result of a sequence of constructive and destructive interferences. The gif on this page really helped: http://www.acs.psu.edu/drussell/demos/superposition/superposition.html

 

[needingtoknow]

Thanks for your time and effort nsaspook!

 

[BvU]

Perhaps needy's understanding is helped by contemplating the following:

Note that what's traveling in a wave is not the particles, air molecules, water molecules or what have you: these make small oscillations around some equilibrium position.

A standing wave isn't bobbing up and down. It's standing. What's bobbing up and down is the what have you's that are passing on some form of energy that brings them away from their equilibrium position.

A traveling wave is something of a misnomer: on the beach there isn't really a whole load of water coming at you. The water itself is making circular motions.