• Pixel-art sticker of Shoalon, personifying Shallow-Water Waves, with the caption “Shallow Water, Slower Wave.”

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Shoalon

Shallow-Water Waves Physics

\[v = \sqrt{g h}\]
Regular price $4.99 USD
Regular price Sale price $4.99 USD
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Meet Shoalon, an ocean wave who slows and stands tall as the sea floor rises. In shallow water a wave's speed is the square root of g times depth: about 198 m/s over 4,000 m of ocean, 3.1 m/s at 1 m. Slowing fronts pile up and break. 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 Shoalon, an ocean wave who slows down and stands up tall as the sea floor rises to meet him.

When a wave's length is much longer than the water is deep, the whole column of water from surface to sea floor moves with it. The floor then controls the wave's speed. Deeper water lets it race, and shallow water holds it back.

The speed of such a wave is v = √(gh). In the open ocean, 4,000 m deep, v ≈ √(9.81 × 4000) ≈ 198 m/s, about 710 km/h. At a depth of 1 m it is only about 3.1 m/s.

As a wave moves into shallower water its front slows first, and the water behind catches up and piles higher. That is why waves rise steeply before they break on a beach.

Tsunamis are the most dramatic case. Their wavelengths are hundreds of kilometres, so even the deep ocean counts as shallow, and they cross whole oceans in less than a day.

Equations

\[v = \sqrt{g h}\]
Symbols
SymbolMeaningUnit
\(v\) wave speed \(\mathrm{m/s}\)
\(g\) acceleration due to gravity \(\mathrm{m/s²}\)
\(h\) water depth \(\mathrm{m}\)