Researching Open Air Column Resonance - Surprising Results

[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?

 

[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.

 

[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.

 

[Danger]

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

 

[cleb]

Thanks anyway!

 

[cleb]

Anyone else?

 

[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.

 

[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.

enjoy your further research
maimonides

Hint: don´t forget the end corrections

 

[cleb]

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

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.

enjoy your further research
maimonides

Hint: don´t forget the end corrections

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!

 

[Dadface]

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!

So was your original intention to study some of the principles of wind instruments? If so it seems that you obtained results that are more relevant to percussion instruments.I think that makes it more interesting.Maimonides said your results are good so why not use them as well as returning to other experiments?