Waves and sound · Model
Waves on water: what a wave is
A wave crosses a pond in seconds. Drop a cork in and it bobs a hundred times and stays exactly where you put it. Both of those are true at once, and the second one is the more useful.
Start here
The wave crosses the whole pond. The gull does not.
A gull is sitting on open water. A line of waves comes in under it, one after another, for a full minute. The waves reach the far side. The gull is exactly where it started.
Something clearly travelled from one side to the other. What was it?
The water did not go anywhere. Each patch of it lifted and dropped and finished where it began, and so did the gull. What crossed the pond was the disturbance — the pattern of lifting and dropping, handed on from one patch of water to the next, carrying energy with it. That travelling disturbance is a wave.
A wave is a disturbance that travels, carrying energy from one place to another without carrying the material with it. On water the disturbance is an undulation: the surface rises into a crest and drops into a trough, over and over. The water itself moves up and down — at right angles to the direction the wave is travelling — which is what makes a water wave a transverse wave.
Two measurements describe the shape of it, and they are independent of each other. The amplitude is how far the surface rises above the still level, measured in millimetres or metres. The wavelength is the distance from one crest to the next crest, measured the same way. Changing one does not change the other.
The figure
Pick a part to measure
Nothing is marked yet. This wave is drawn to one scale in both directions: 0.40 m from crest to crest, and 0.08 m from the still level up to a crest.
At the bench · a ripple tank one metre across
One paddle. Two things you can change about it.
Move a control to begin
A motor dips a paddle into one end of the tank. How deep it dips, and how far apart it lays the crests, are set separately. A float sits at the middle of the tank.
Commit first. The paddle dips deeper but keeps exactly the same rhythm. What happens on the water?
20 mm
300 mm
Amplitude
—
above the still level
Wavelength
—
—
The float rises and falls through
—
and stays in the same place
Steepness
—
Key fact
A wave carries energy from place to place without carrying the material with it. On water the surface rises into crests and drops into troughs at right angles to the direction of travel, which makes it transverse. Amplitude is the rise above the still level; wavelength is the distance from one crest to the next. Neither one sets the other.
Think again
“The water travels along with the wave.”
Drop a cork in a tank and send a hundred waves under it. The cork bobs a hundred times and ends up where it started. If the water were travelling, the far end of the tank would fill up and the near end would empty, and a swimmer would be carried out to sea by every passing swell. What travels is the disturbance, handed from each patch of water to the next; each patch lifts its neighbour, gets lifted in turn, and settles back. Energy moves across the tank. Water does not.
“A bigger wave is a longer wave.”
Two different measurements are hiding inside the word bigger. Amplitude is how far the surface lifts; wavelength is how far apart the crests are. A wave can be tall and short — a steep chop with crests a hand's width apart — or low and long, like an ocean swell that lifts a boat a few centimetres over a hundred metres. The bench above sets the two independently, and moving one leaves the other exactly where it was.
Mastery ladder
Not started yet.
Rungs 3 and 4 you mark yourself.
Rung 1 · Read the wave
A wave on a tank has crests 0.60 m apart. A float on it rises 0.05 m above the still level and drops 0.05 m below it. Give the wavelength and the amplitude.
Rung 2 · The one that catches people
Waves pass under a gull for a minute and the gull finishes exactly where it started. Which statement is right?
Rung 3 · Explain
A cork floats in a ripple tank while waves cross from one end to the other. Explain what the cork does and what the wave does, using the words disturbance, energy and transverse.
Rung 4 · Take it somewhere new
A crowd in a stadium sends a wave right round the ground in 40 seconds, and nobody leaves their seat. Say what plays the part of the amplitude and what plays the part of the wavelength, then give one way this is not like a wave on water.
Key note
A wave is a travelling disturbance that carries energy from place to place without carrying the material with it. Waves on water are undulations: the surface rises into crests and drops into troughs, moving at right angles to the direction the wave travels, which makes them transverse. Amplitude is the rise above the still level and wavelength is the distance from one crest to the next; changing one does not change the other.
Going further
The independence of amplitude and wavelength is what makes deep-ocean tsunamis so dangerous. Out over deep water a tsunami has an amplitude of well under a metre and a wavelength that can reach 200 km, which is a steepness of about 1 in 200 000 — a ship rides over it and the crew notice nothing at all. The energy is still there; it is simply spread through a very long, very low undulation. When that undulation reaches shallow water it slows, the back of it catches the front, and the same energy is repacked into something short and tall.
One honest limit of the picture drawn above: the water in a wave does not move in a straight line up and down. Each patch travels round a small near-circle, forward at the crest and backward in the trough, returning to about where it began. The straight up-and-down version is close enough to see what transverse means, and it is what the bench draws, but a diver watching sand grains under a swell sees the circles.
Before this lesson
- Nothing — this is where the unit starts.
Connects to
At GCSE this becomes
- Frequency and period, the wave equation linking wave speed to frequency and wavelength, and measuring wave speed in a ripple tank.
Where to next
Ask Mr Badmus AI
Got a wave of your own to describe — a rope, a pond, the sea?
The tank is a teaching model. Both figures are drawn to a single scale in both directions, so the steepness you see is the steepness the numbers claim; the tank is taken as exactly 1.00 m across and the float as weightless, riding the surface without disturbing it. The paddle is treated as making one steady train of identical waves, which a real paddle only approximates. The roughly 1-in-7 limit at which a crest spills over and breaks is an approximate figure for deep water and shifts with depth, wind and how the wave was made. Real water in a wave moves round small near-circles rather than straight up and down.
Lesson content © MrBadmusAI.