The big idea: Flick one end of a long rope and a hump races to the far end — but the rope itself stays put, each bit only jerking up and down as the pulse goes by.
Energy moves, particles stay: A wave carries energy along while the particles just vibrate on the spot.
There are two ways a particle can vibrate compared with the wave's direction of travel: across it (transverse) or along it (longitudinal).
New words — define them now: Transverse wave: the particles vibrate perpendicular (at right angles) to the direction the wave travels. Example: light, and a wave on a rope.
Longitudinal wave: the particles vibrate parallel (back and forth along the same line) to the direction the wave travels. Example: sound.
Transverse (across)
- Particles move perpendicular to the wave's travel
- Shows crests (tops) and troughs (bottoms)
- Examples: light, water surface, a rope wave
Longitudinal (along)
- Particles move parallel to the wave's travel
- Shows compressions (squashed) and rarefactions (stretched)
- Examples: sound, a push-pull on a spring
More new words: In a longitudinal wave, a compression is where the particles are bunched close together (high pressure); a rarefaction is where they are spread apart (low pressure).
The nature of sound: Sound is a longitudinal mechanical wave: the air (or water, or solid) particles vibrate back and forth along the direction of travel.
Compressions are regions of higher pressure, rarefactions of lower pressure. Sound needs a medium: it cannot cross a vacuum.
The one thing to hold on to: Ask: which way does a particle move compared with the wave?
At right angles → transverse. Back and forth along the same line → longitudinal.
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For any wave, one particle's displacement–time graph shows how that particle moves.
What you read from it
- The amplitude — the peak.
- The period — one full cycle.
- The period links to the frequency and wave speed through the data-booklet wave equation.
- wave speed (m s⁻¹)
- frequency — cycles per second (Hz)
- wavelength — one full cycle (m)
- period — time for one full cycle (s)
Which graph gives which length?: A displacement–time graph of one particle → read the period T (a time).
A displacement–distance snapshot of the whole wave → read the wavelength λ (a length).
Both look like the same wavy shape, so always check the x-axis label first.
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Where are the compressions?
Which particle moves fastest?: On a snapshot, the particles at the rest line (displacement zero) are moving fastest; the ones at a crest or a trough are momentarily still, just as in SHM.
A particle on a wave has a displacement–time graph that peaks at 4.0 cm and repeats every 4.0 s. Find the amplitude, the period and the frequency of the wave.
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How this is tested — usually a quick one-mark Paper 1A read-off or deduction:
Paper 1A — read a graph
- Off a displacement–time graph of one particle, read the amplitude and frequency.
- Off a displacement–distance snapshot, read the wavelength.
Paper 1A — deduce motion
- Given a snapshot and how one point moves next, work out the wave's direction of travel and how another point is moving.
The classic trap: Confusing a snapshot (x-axis = distance → wavelength) with a displacement–time graph (x-axis = time → period).
The trick for 'which way is it moving?': On a transverse snapshot, a point takes on the displacement of the point just behind it (the side the wave came from).
So if the wave travels right, each point is about to copy the point on its left — look just to the left to see whether the point next goes up or down.
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A transverse wave travels to the right. A snapshot (displacement–distance graph) shows the pattern repeating every 4.0 m, with a peak of 4.0 cm. Point P sits on the rising part of the curve, just to the right of a crest. Find the wavelength and state which way point P moves next.
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