Surfer's Wait: The Period of a Wave

An educational simulation game. Predict how long a surfer waits between waves, how many waves come each minute, how fast a swell moves, how far apart its crests are, and its frequency, then watch the swell roll in, sped up.

PeriodOcean waves

SURFER'S WAIT

The wait between waves

Ready
Enable JavaScript to bring in the swell. The instructions and worked example remain readable.
SeaSurfer and crestsYour predictionRuler and beach
WavesT = λ ÷ v

Time

0.00 s

t

Period

— s

T = λ ÷ v

Wavelength

— m

λ

Swell speed

— m/s

v

Crests so far

—

n

Predict before you start

Type your prediction to set things up. Start stays off until there is an answer.

Predict how the swell arrives.

Mission score—

Every answer must be within 2%: each earns 100 points. Getting it right on the first run adds 50. A run counts as soon as it starts.

✓ Right answer① First try

How to play Surfer's Wait

  1. Choose a test and read the spacing, the speed, or the period on the card.
  2. Use T = λ ÷ v, λ = v·T, and f = 1 ÷ T; a minute holds 60 s ÷ T waves.
  3. Type your prediction and press Start. The swell rolls in, sped up.
  4. Compare the orange lines with the crests' dots on the right, or the orange marks with the crests in the sea.

The period of a wave

The period T of a wave is the time it takes for one whole wave to pass a point: for a surfer waiting beyond the breakers, the time between one crest lifting the board and the next. During one period the wave travels exactly one wavelength, so T = λ ÷ v, or turned round, λ = v·T and v = λ ÷ T. The frequency is the period upside down, f = 1 ÷ T: an 8 s swell has a frequency of 0.125 Hz, and 7.5 waves arrive each minute. Surfers and sailors care a lot about the period. Swell made by a distant storm has long periods, 10 to 20 s, long wavelengths, and moves fast; it arrives in smooth, powerful lines. A local wind chop has short periods of a few seconds and feels messy. The period is also the easiest number to measure: stand still, count the seconds between crests, and you have it, whatever the waves are made of.

A focused learning model

The swell is an ideal sine wave of one period, rolling in without breaking or losing height; the surfer only rises and falls. Heights are drawn larger than lengths. Time runs faster than real time by the factor shown, so each run lasts about 4 s; the clock shows the real time. The first crest reaches the surfer half a period after the start. Answers within 2% are right.

Changing language keeps your test, prediction, attempts, and run.