• Pixel-art sticker of Echola, personifying Echolocation, with the caption “There And Back, Halve It.”

IndexForces & FieldsSticker

Echola

Echolocation Physics

\[d = \frac{v\,t}{2}\]
$4.99 USD
$4.99 USD
Sale Sold out

Meet Echola, a bat who finds objects by timing echoes. Sound must go there and back, so the distance is half of speed times time: a 2 s echo in air at 343 m/s means a wall 343 m away. The art draws the pulses and echoes in code. 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 Echola, a bat who measures the world by shouting and listening.

Sound travels at a steady speed through still air. Send a short pulse toward a wall and some of it bounces back as an echo. The echo has travelled to the wall and back, so the distance to the wall is half the total path: d = vt/2. Bats use rapid high-pitched calls to do this many times a second, building a picture of insects and obstacles. Donald Griffin coined the word echolocation in 1944.

In air at about 20 °C, sound travels at roughly 343 m/s. If an echo returns after 2 s, the sound went 343 × 2 = 686 m in total, so the wall is 686 / 2 = 343 m away.

Ships use sonar the same way in water, where sound is much faster, about 1,480 m/s. Parking sensors, ultrasound scanners and depth sounders all time echoes.

Forgetting to halve the time is the classic mistake. The speed of sound also changes with temperature, so precise ranging corrects for it.

Equations

\[d = \frac{v\,t}{2}\]
SymbolMeaningUnit
\(d\) distance to the reflecting object \(\mathrm{m}\)
\(v\) speed of sound \(\mathrm{m/s}\)
\(t\) time for the echo to return \(\mathrm{s}\)

Sources

  1. OpenStax University Physics Vol. 1 — Speed of Sound
  2. Wikipedia — Animal echolocation

Field notes

View all
  • Pixel-art illustration for this Pixelated Physics post: two pixel crowds: fermion characters each standing alone in their own boxes, and boson characters happily piling together into one box

    What Is the Spin–Statistics Theorem?

    The spin–statistics theorem ties a particle’s spin to the symmetry of its quantum state. Integer spin → bosons (symmetric); half-integer spin → fermions (antisymmetric). Fierz (1939) and Pauli (1940) made...

    What Is the Spin–Statistics Theorem?

    The spin–statistics theorem ties a particle’s spin to the symmetry of its quantum state. Integer spin → bosons (symmetric); half-integer spin → fermions (antisymmetric). Fierz (1939) and Pauli (1940) made...

  • Pixel-art illustration for this Pixelated Physics post: a pixel pendulum bob character swinging over a circular floor marked with pixel pegs, a few pegs knocked over showing the swing plane slowly turning, a pixel Earth spinning in the window

    How Does a Foucault Pendulum Prove Earth Rotates?

    A long pendulum’s swing plane slowly turns relative to the floor. Foucault showed in 1851 that the turn is Earth’s rotation made visible. The rate is 360° times the sine...

    How Does a Foucault Pendulum Prove Earth Rotates?

    A long pendulum’s swing plane slowly turns relative to the floor. Foucault showed in 1851 that the turn is Earth’s rotation made visible. The rate is 360° times the sine...

  • 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...

1 3
View all