• Pixel-art sticker of Flutel, personifying Open Pipe Resonance, with the caption “Open Both Ends, Every Harmonic.”

IndexForces & FieldsSticker

Flutel

Open Pipe Resonance Physics

\[f_n = \frac{n v}{2L}\]
$4.99 USD
$4.99 USD
Sale Sold out

Meet Flutel, a brass tube open at both ends who can sing every harmonic. Open ends allow frequencies nv/(2L), so a 0.50 m pipe in 20 °C air sounds 343, 686 and 1029 Hz. A pipe closed at one end plays only odd harmonics, an octave lower. Pixel-art kiss-cut sticker in 2, 3, 4 and 6 inches; equation, symbols and sources in the physics panel below.

Size
Surface

Flat $6 shipping worldwideMade to order, ships in 2–5 business days

Details

Size3″ × 3″

3″ × 3″ kiss-cut sticker.

Shipping

Flat $6 shipping on every order, worldwide, whatever's in it.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

Full refund & replacement policy

The physics

Meet Flutel, a brass tube open at both ends who can sing every note in his family.

Air in a pipe can vibrate in standing waves. At an open end the air moves freely, so each open end must be a place of biggest motion. The simplest wave that fits has half a wavelength along the pipe.

The allowed frequencies are fₙ = nv/(2L), where n = 1, 2, 3 and so on. In air at about 20 °C, sound travels at 343 m/s. For a pipe 0.50 m long the lowest note is 343 Hz, and the next ones are 686 Hz and 1029 Hz, all whole-number multiples.

A pipe closed at one end is different. It only makes odd multiples, and its lowest note is an octave lower than the same pipe left open.

Flutes and many organ pipes work like Flutel. Players change notes by opening holes, which changes the length of air that is vibrating.

Equations

\[f_n = \frac{n v}{2L}\]
SymbolMeaningUnit
\(f_n\) frequency of the nth harmonic \(\mathrm{Hz}\)
\(n\) harmonic number \(\mathrm{dimensionless}\)
\(v\) speed of sound in air \(\mathrm{m/s}\)
\(L\) length of the pipe \(\mathrm{m}\)

Sources

  1. OpenStax University Physics Vol. 1 — Sources of Musical Sound
  2. Wikipedia — Acoustic resonance

Field notes

View all
  • Pixel-art Einstein ring: a foreground galaxy bends the light of a galaxy directly behind it into a circular ring of arcs centered on it

    How Does Gravity Bend Light? Einstein Rings and...

    Gravity bends light because spacetime is curved. The 1919 eclipse measured the Sun’s deflection; Einstein’s 1936 note foresaw stellar lenses; modern telescopes image Einstein rings. Here is the physics without...

    How Does Gravity Bend Light? Einstein Rings and...

    Gravity bends light because spacetime is curved. The 1919 eclipse measured the Sun’s deflection; Einstein’s 1936 note foresaw stellar lenses; modern telescopes image Einstein rings. Here is the physics without...

  • Pixel-art illustration for this Pixelated Physics post: three abstract pixel mascots of early quantum ideas: a glowing light-packet character, a tiny atom with stepped orbit rings, and a fuzzy uncertainty cloud, climbing a staircase of energy levels

    Who Started Quantum Mechanics? Planck, Bohr and...

    Quantum theory did not begin with one paper. Planck quantized energy in 1900, Bohr quantized the atom in 1913, and Heisenberg’s 1925 matrix mechanics plus the 1927 uncertainty relation made...

    Who Started Quantum Mechanics? Planck, Bohr and...

    Quantum theory did not begin with one paper. Planck quantized energy in 1900, Bohr quantized the atom in 1913, and Heisenberg’s 1925 matrix mechanics plus the 1927 uncertainty relation made...

  • Pixel-art illustration for this Pixelated Physics post: a pixel star character opening up like a treasure chest to reveal it is mostly hydrogen bubbles with some helium, a glowing spectrum rainbow strip with dark lines beside it

    Did Cecilia Payne Discover What Stars Are Made Of?

    Cecilia Payne’s 1925 thesis showed that stars differ mainly in temperature, not composition, and that hydrogen and helium vastly outnumber everything else. She then called that result “almost certainly not...

    Did Cecilia Payne Discover What Stars Are Made Of?

    Cecilia Payne’s 1925 thesis showed that stars differ mainly in temperature, not composition, and that hydrogen and helium vastly outnumber everything else. She then called that result “almost certainly not...

1 3
View all