# Open air columns

1. Sep 9, 2010

### cleb

I am doing research on open air column resonance. In an experiment I suspended copper pipe and struck it with a hammer. I measured the fundamental frequency for many lengths of pipe.

After analyzing the data, I was surprised with the relationship. My research indicated that I would use the formula $$f=\frac{nv}{2L}$$. My data, however, seems to follow something like $$f=\frac{c}{L^{2}}$$ where $$c$$ is some constant.

Does anyone know what's going on?

2. Sep 9, 2010

### Danger

Welcome to PF, Cleb.
I'm not a scientist, and know nothing of formulae, but I do have to ask an obvious question here. Is your first equation based upon the cylinder alone? If so, might you have failed to account for the rigidity and placement of the suspension point? No insult intended; it's just the first thing that came to mind.

3. Sep 9, 2010

### cleb

Thanks, I forgot to mention that in my first post. The pipe was suspended by fishing line was able to vibrate freely. In addition, when I use a frequency generator, the frequencies sound right, which obviously isn't a valid way to measure frequency, but it does lead me to believe that my measured frequencies are correct, and it is not an error of pipe restraint or microphone placement.

4. Sep 9, 2010

### Danger

Okay. In that case, I'm afraid that you'll have to wait for someone else to respond. That was my best shot.

5. Sep 9, 2010

### cleb

Thanks anyway!

6. Sep 10, 2010

### cleb

Anyone else?

7. Sep 10, 2010

### pallidin

My 2-cents:
Formulae are usually derived with respect to specific experimental parameters.
If you design an experiment using some of those parameters, but altering others, there is no reason to expect the result to follow the "standard" formulae.

I don't know if that made any sense.

8. Sep 11, 2010

### maimonides

Hello cleb
I think you´ve done good work and your measurements agree with theory.
But: What you have measured are the resonancess of the tubes, not of the air columns in the tubes.
(You will find this covered as vibration of long, thin bars in texts on acoustics or vibration, eg. Fletcher/Rossing, The Physics of Musical Instuments. Theory predicts inverse square dependence of resonant frequency on length, all other things being equal)
You´d better use a different way of exciting air column vibrations:
- loudspeaker with frequency generator (use your computer/soundcard)
- insert a tight fitting cork und pull it out as fast as possible
- you might try blowing it like a panflute ( not easy with open tubes)
and dampen tube vibrations with a rag.

maimonides

Hint: don´t forget the end corrections

9. Sep 11, 2010

### cleb

Thank you, pallidin, but I think maimonides hit the nail on the head.

Technically, my experiment was founded on instrument making, I just had the wrong type of resonance it seems. Thank you for helping me out on this!

10. Sep 11, 2010