# Resonance and air columns open at one end and closed at the other.

1. Oct 23, 2007

### Spookie71

1. The problem statement, all variables and given/known data
The question I'm working on is
First the diagram:http://http://i215.photobucket.com/albums/cc10/Spookie71/image0-12.jpg

There is the matter of the equation I use to solve the equation:
Can you please explain for me?

Scott

2. Oct 23, 2007

A resonance is not a part of the diagram. The entire diagram is of one particular resonance.

In order to draw a resonating wave, all you have to do for this situation (open and free ends) is make sure that the node is at the closed end and the antinode is at the free end. The first resonance refers to the situation where there's half a full loop. (Top one in this picture: http://www.umanitoba.ca/faculties/arts/linguistics/russell/138/sec4/sh2-15.gif [Broken] )

The second resonance refers to the situation where there's a two nodes and two antinodes (one loop and a half). This is the second way of making sure that there's a node at one end and an antinode at the third end.

Here's an analogy:
You're a physics teacher and your boss tells you to make a line of students. He INSISTS that the first person be male and the last person be female. The simplest way of doing this is to make a line using one male student and one female student. This is your first solution.
If he comes back and says "Don't be lazy! Find a different way!" then you can put one male, another student, and one female in a line. This would be your second solution.

If you think of the first person being male and the last being female that's like having the ends open and closed. If those weren't the case then the waves would just go crazy and not resonate (not keep the node positions and whatnot). The first solution would be the first resonance and the second solution would be the second solution, etc etc.

As for lengths, I would never use a formula. I'd much rather draw it and figure out the ratio between the length and the wavelength.

Last edited by a moderator: May 3, 2017
3. Oct 24, 2007