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Waves are one of the most pervasive phenomena in physics. From the ripples on a pond to the light reaching your eye from a distant galaxy, from the sound of a spoken word to the pulses travelling along a nerve fibre, waves carry energy and information across space without the bulk transport of matter. Module 4.4 of the OCR A-Level Physics A specification (H556) — Waves — asks you to understand wave motion at a level which will underpin everything you subsequently study in optics, quantum physics, communications and modern physics.
This lesson introduces progressive waves, the distinction between transverse and longitudinal waves, and the essential vocabulary you will use for the rest of the module.
Informally, a wave is a disturbance that travels through a medium (or through space) transferring energy from one place to another without transferring matter.
That definition contains three essential ideas, and each deserves scrutiny:
This last point is the most common source of confusion for students beginning A-Level. When a water wave moves across a pond, a floating cork bobs up and down but does not travel with the wave. The wave carries energy horizontally; the cork's motion is (approximately) vertical. Similarly, when sound travels across a room, air molecules oscillate about their equilibrium positions by a tiny fraction of a millimetre — they do not drift from the speaker to your ear.
Exam Tip: If an OCR question asks you to "explain what is meant by a progressive wave", your answer must include both ideas: (1) energy is transferred through the medium, and (2) particles of the medium do not move with the wave — they oscillate about equilibrium.
A progressive wave (sometimes called a travelling wave) is one in which the disturbance travels through space, carrying energy with it. This is contrasted with a stationary wave (Lesson 11), in which energy is stored but not transmitted.
For a progressive wave:
Consider a long rope with one end shaken up and down. The shake creates a pulse which propagates along the rope. Every particle of the rope moves vertically — up and then down — and each particle starts its motion a fraction of a second after its neighbour. The result is a travelling hump that moves along the rope at a speed determined by the tension and mass per unit length of the rope.
flowchart LR
S[Source oscillates] --> P1[Particle 1 pulled up]
P1 --> P2[Particle 2 pulled up later]
P2 --> P3[Particle 3 pulled up later still]
P3 --> P4[Pattern appears to move]
P4 --> E[Energy transferred along rope]
P4 --> M[No net motion of matter]
A transverse wave is one in which the oscillations (displacement of particles) are perpendicular to the direction of energy transfer.
Examples include:
A characteristic property of transverse waves is that they can be polarised — because the oscillations are perpendicular to propagation, they can be restricted to a single plane. This is the key experimental evidence that light is a transverse wave, as you will see in Lesson 4.
A longitudinal wave is one in which the oscillations (displacement of particles) are parallel to the direction of energy transfer.
The disturbance consists of alternating regions of compression (where particles are pushed together) and rarefaction (where particles are spread apart). The compressions and rarefactions travel through the medium at the wave speed, while each individual particle oscillates back and forth about its equilibrium position along the line of travel.
Examples include:
Longitudinal waves cannot be polarised, because the oscillation is already along a single direction (the direction of travel); there is nothing further to restrict. This is a useful test: if you can polarise it, it is transverse; if you cannot, it is longitudinal.
| Feature | Transverse | Longitudinal |
|---|---|---|
| Direction of oscillation | Perpendicular to propagation | Parallel to propagation |
| Can be polarised? | Yes | No |
| Examples | Light, EM waves, waves on a string, water waves, S-waves | Sound, P-waves, compression waves on a slinky |
| Can travel through vacuum? | Only EM waves | No |
| Visual appearance | Crests and troughs | Compressions and rarefactions |
| Displacement graphed against position | Sine curve | Sine curve (of displacement) |
Note the last row: although longitudinal waves look very different physically, their displacement–position graph looks just the same as that of a transverse wave — a sinusoid. This is because we plot the signed displacement of each particle from equilibrium, whether that displacement is along the direction of travel or across it.
Exam Tip: The OCR specification explicitly requires you to "give examples of transverse and longitudinal waves" and to "describe the differences between transverse and longitudinal waves". Practise a one-sentence answer for each.
All waves originate in some oscillation at a source. A loudspeaker cone vibrating backwards and forwards compresses the air in front of it, creating a longitudinal sound wave. An electron oscillating in an aerial generates an electromagnetic wave. A stone dropped into a pond disturbs the water surface, creating a transverse ripple. The frequency of the source determines the frequency of the wave; the medium determines the speed; the wavelength is what you get from combining the two.
This is worth emphasising because students sometimes imagine that the wave speed is controlled by the source. It is not. A violin string and a cello string both produce sound waves in air at the same speed (~340 m s⁻¹), even though the strings themselves vibrate at very different frequencies. The wavelengths of the resulting sound waves differ to match.
A wave transfers energy. For a wave of a given type, the energy transferred per unit time (the power) is proportional to the square of the amplitude:
P ∝ A²
This is why a loud sound requires much more energy than a quiet one — doubling the amplitude quadruples the power. It also explains why distant sources appear faint: as a wave spreads out from a point source, the energy is distributed over a larger area (a sphere of surface area 4πr²), and the intensity falls as the inverse square of the distance:
I = P / (4πr²)
You will return to this inverse square law when you study electromagnetic radiation from stars in Module 5.
Q. Classify each of the following as transverse or longitudinal: (a) ultrasound in water, (b) microwaves in air, (c) a ripple on a pond, (d) vibration of a guitar string, (e) a seismic P-wave.
A.
(a) Longitudinal — sound (including ultrasound) is always longitudinal. (b) Transverse — all electromagnetic waves, including microwaves, are transverse. (c) Transverse — water waves are (approximately) transverse, with particles moving vertically. (d) Transverse — the string moves perpendicular to its length. (e) Longitudinal — P-waves are primary (pressure) waves, which are longitudinal. (S-waves, by contrast, are transverse shear waves.)