The big idea: A wave carries energy along, but the particles of the medium just vibrate on the spot — they don't travel with the wave.
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 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.
For any wave, one particle's displacement–time graph shows how that particle moves. From it you read the amplitude (the peak) and the period (one full cycle), and 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.
Worked example — read a displacement–time graph
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.
Solution
- The amplitude is the peak displacement read straight off the graph:
- The period is the time for one full cycle (the repeat time):
- Frequency is one over the period — start with the given wave equation:
- Put in the period and work it out — keep the unit:
Final answer
amplitude = 4.0 cm, period T = 4.0 s, frequency f = 0.25 Hz.
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How this is tested: This is usually a Paper 1A multiple-choice question — a quick one-mark read-off or deduction.
- Read a graph: off a displacement–time graph of one particle, read the amplitude and frequency; off a displacement–distance snapshot, read the wavelength. - 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.
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.
IB-style question — wavelength & particle direction from a snapshot
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.
Solution
- The wavelength is one full repeat along the distance axis, read off the snapshot:
- The wave moves right, so each point copies the point just to its left.
- Just to the left of P is the crest (a higher displacement), so P is about to rise toward it.
- Therefore P moves upward next (toward the crest).
Final answer
wavelength λ = 4.0 m; point P moves upward next (it takes the displacement of the point on its left, which is higher).