• Dopplerine physics mug, rotating view
  • Dopplerine physics mug, close-up
  • Dopplerine – Doppler Effect pixel-art physics mug, black ceramic, view 1
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  • Dopplerine – Doppler Effect pixel-art physics mug, black ceramic, view 4
  • Dopplerine – Doppler Effect pixel-art physics mug, black ceramic, view 5
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DopplerineDoppler EffectMug

Dopplerine – Doppler Effect Physics Mug

$21.99 USD
$21.99 USD
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Shipping calculated at checkout. Free US shipping · $10 flat shipping outside the US.
Size
11oz · 15oz
Made
To order · shipping times

Why does a siren drop in pitch as it passes? Dopplerine rides the waves. A source moving toward you bunches its wavefronts, so you hear a higher frequency; moving away, they spread and the pitch falls. For sound, f = f0(v + vo)/(v − vs) for approach. Pixel-art black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Size

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

ShippingFree US

Free US shipping. $10 flat shipping outside the US.

Made to order: about 10 days of production and handling before it ships.

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

Dopplerine rides the waves, and you can hear her coming.

A siren rising as it approaches and dropping as it passes is the Doppler effect, first described by Christian Doppler in 1842. A source moving toward you emits each wave crest a little closer to you than the last, so the crests arrive bunched together: higher frequency, higher pitch. Moving away, they arrive spread out, and the pitch falls.

The formula on this mug is for sound, which travels through air at a fixed speed v. Speeds count as positive when source and observer move toward each other, as in COMING IN HIGH; flip their signs for LEAVING LOW.

The same idea applies to light, with a relativistic formula. Light from a star moving away from us is shifted to the red, and from one approaching us to the violet, which is how astronomers measure the motions of stars.

Dopplerine never changes her tune. You just hear it differently depending on which way she is going.

Equations

\[f = f_0\,\frac{v + v_o}{v - v_s}\]
SymbolMeaningUnit
\(f\) frequency heard by the observer \(\mathrm{Hz}\)
\(f_0\) frequency emitted by the source \(\mathrm{Hz}\)
\(v\) speed of sound in the medium \(\mathrm{m/s}\)
\(v_o\) observer speed, positive when moving toward the source (negative when moving away) \(\mathrm{m/s}\)
\(v_s\) source speed, positive when moving toward the observer (negative when moving away) \(\mathrm{m/s}\)

Sources

  1. HyperPhysics — Doppler Effect for Sound
  2. Encyclopaedia Britannica — Doppler effect
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Field notes

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