# I Tone vs hole size & spacing in a short tube

#### JT Smith

Summary
tone produced by blowing into a cylindrical tube with small, regularly spaced holes at one end
While trying to dislodge some stubborn coffee debris in the holes of a wet espresso bottomless portafilter by blowing into it I discovered that it produced a tone at just over 3000Hz, with harmonics. I wondered, is there some way to use that to determine something about the hole size and spacing? Or is it more complicated than that?

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#### member659127

The fundamental frequency generated by a tube depends on the tube length via a very simple equation. However before going into details are you sure the portafilter can be treated as a tube? It looks more like a membrane? Where exactly are you blowing from?

#### JT Smith

I'm blowing from the top. The "tube" is about 6cm long. Diameter at the top, where it's open, is about 6cm. It's cylindrical but then tapers over the last 1.5cm near the bottom to 4.5cm in diameter. There are at least 150 holes spaced evenly about 2mm apart. I think the holes are about 0.25mm in diameter. It doesn't produce a tone when it's dry.

#### member659127

That's the theory you need: https://www.compadre.org/osp/EJSS/4492/277.htm
(Both ends open part)

Diameter doesn't matter. the one and the only one crucial thing to know is the length. You say "about 6 cm" for that. The formula gives "about 2800 Hz" in that case which is near to your 3000. Since you say it is "just over" 3000 I bet the length is "just below" 5.6 cm. I mean that is the part that resonates. Small holes and other stuff are irrelevant.

(Since it seems it is both ends open you will hear all the harmonics. If one end was closed you would hear 1500 Hz and only the odd harmonics)

#### member659127

It doesn't produce a tone when it's dry.
That also makes sense. I play traditional reed flute, when you wet it much easier to play...

#### JT Smith

Okay, thank you for the explanation. I know about standing waves in a tube but thought this was a different problem related to the holes, maybe akin to the whistle on a teapot. I was hoping it would be a clever way to measure the hole size. The actual working length is probably affected by my mouth/lips being inserted into the top to form a seal.

Thanks again.

#### member659127

maybe akin to the whistle on a teapot
Well that is really a complicated domain:
https://en.wikipedia.org/wiki/Physics_of_whistles

When practicing the reed flute first time and trying to make a proper sound; the first thing we were trying was to avoid "whistling" which is always a risk for a beginner. Distinguishing it from the proper tone is important.

Completely different physics there, it involves fluid dynamics not standing waves.

#### JT Smith

Yes, I'd looked at some of that prior to posting and realized it was too complicated for me to parse. Hence my question on this forum. Fortunately none of this matters when it comes to making espresso. I was just curious.

"Tone vs hole size & spacing in a short tube"

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