OxfordAQA International AS and A-level Physics: Progressive waves, longitudinal and transverse waves, polarisation (9630) – Revision Notes

These notes condense sections 3.5.3 (Progressive waves) and 3.5.4 (Longitudinal and transverse waves) of the OxfordAQA International AS and A-level Physics (9630) specification, Version 4.4. Both sections are shared AS and A-level content. For full explanations and longer worked examples, read the study guide, then test yourself with the practice questions. The course hub and checklist show where this unit sits in the course.

Key definitions

• Progressive wave: a wave that carries energy onward while the medium itself stays in place.
• Displacement: distance of a particle from its equilibrium position, in a stated direction.
• Amplitude (A): maximum displacement from the equilibrium position.
• Wavelength (λ): distance between two adjacent points oscillating in phase.
• Period (T): time for one complete oscillation of a particle.
• Frequency (f): number of complete oscillations per second, in hertz.
• Wave speed (c): distance moved by the wave pattern per second.
• Phase difference: the gap in stage between two oscillations, measured as an angle or a fraction of a cycle.
• In phase: phase difference of 0, 2π, 4π and so on. Antiphase: phase difference of π, 3π and so on.

Equations

Equation	Use
f = 1/T	Frequency and period
c = fλ	Wave speed, frequency and wavelength (any wave)
phase difference (cycles) = separation / λ	Two points on the same wave at the same instant
phase difference (rad) = 2π × separation / λ	The same, in radians
phase difference (cycles) = Δt / T	One point at two instants
depth = (speed × delay) / 2	Ultrasound pulse-echo

One cycle = 360° = 2π rad. Half a cycle = 180° = π rad. A quarter cycle = 90° = π/2 rad.

Method: phase difference in four steps

1. Convert the separation (or time gap) to metres (or seconds).
2. Divide by λ (or by T) to get a fraction of a cycle.
3. Multiply by 360 for degrees, or by 2π for radians.
4. State which point lags. The point further along the direction of travel lags.

Worked reminder: points 0.45 m apart on a wave of wavelength 0.60 m.

0.45 / 0.60 = 0.75 cycle = 270° = 3π/2 rad

Two graphs, two jobs

Graph	Read off
Displacement against distance (snapshot)	Wavelength, amplitude
Displacement against time (one particle)	Period, amplitude

Frequency comes from 1/T. Speed comes from fλ, or from λ/T using one reading from each graph.

Which way is a particle moving?

For a transverse wave travelling to the right, a particle just to the right of a crest is on a downward slope. The wave is about to carry the crest to it, so it is moving up. A particle just to the left of a crest is moving down. A particle at a crest or trough is momentarily at rest, and a particle at equilibrium moves fastest. To predict the motion a short time later, slide the whole snapshot a little to the right and see what each particle’s new displacement would be.

Transverse and longitudinal waves

	Transverse	Longitudinal
Oscillation compared with energy travel	At 90°	Along the same line
Features	Crests and troughs	Compressions and rarefactions
Examples	String waves, all electromagnetic waves	Sound
Polarisation	Possible	Not possible

Must-know details:

• Electromagnetic waves are oscillating electric and magnetic fields, perpendicular to each other and to the energy flow. No medium is needed.
• In a vacuum every electromagnetic wave moves at 3.00 × 10⁸ m s⁻¹. Only frequency and wavelength differ.
• Sound is carried by particles, so it cannot cross a vacuum. Air particles oscillate along the direction of travel.
• At the centre of a compression the particles are momentarily moving forwards, with zero displacement.
• Waves on a string: each piece of string moves at right angles to the string’s length while the pulse moves along it.

Ultrasound in medicine

• Ultrasound is sound above the range of human hearing, above about 20 kHz. Imaging uses a few megahertz.
• A probe emits short pulses and detects reflections from boundaries between different tissues.
• Gel between probe and skin removes air. Without it most of the ultrasound would be reflected at the air-skin boundary.
• The time delay of each echo gives the depth of the boundary: depth = (speed × delay) / 2. The factor of 2 is there because the pulse travels there and back.
• Higher frequency gives shorter wavelength and finer detail but weaker penetration, because tissue absorbs it more.

Worked reminder: an echo returns 84 μs after the pulse, with speed 1540 m s⁻¹ in tissue.

depth = 1540 × 84 × 10⁻⁶ / 2 = 0.0647 m = 6.5 cm

Polarisation

• Plane-polarised: oscillation (displacement or electric field) confined to a single plane that contains the direction of travel.
• A Polaroid transmits the component of the oscillation along its transmission axis and absorbs the perpendicular component.
• Two Polaroids with axes parallel pass the light. With axes at 90° (crossed) almost no light passes.
• Rotating the second Polaroid through 360° gives two maxima and two minima.
• Only transverse waves can be polarised. This is the evidence that light and radio waves are transverse. Sound cannot be polarised.
• Aerials: a rod aerial responds to the component of the electric field along its length. Align the receiving aerial parallel to the transmitting one for the strongest signal. At 90° the signal is nearly zero.

Malus’s law is not expected, so you do not need to calculate transmitted intensity from the angle.

Must-know distinctions

• Frequency (set by the source, unchanged when the wave enters a new medium) against wavelength and speed (change with the medium).
• Particle speed (changing as the particle oscillates) against wave speed (constant in a given medium).
• Period (one particle, time) against wavelength (the wave pattern, distance).
• Unpolarised (many directions) against plane-polarised (one direction).
• Reduced intensity against polarised. A Polaroid absorbs part of unpolarised light, and the light that gets through is plane-polarised.

Quick self-test

1. The oscillation of a particle in a wave has period 0.025 s. Find its frequency.
2. A sound wave has frequency 1.2 kHz and wavelength 0.28 m. Find the speed.
3. Two points 0.45 m apart lie on a wave of wavelength 0.60 m. State the phase difference in degrees and radians.
4. A particle has period 16 ms. Find the phase difference between its motion at two instants 6.0 ms apart, in degrees and radians.
5. An echo returns 68 μs after a pulse, and sound travels at 1540 m s⁻¹ in the tissue. Find the depth of the reflecting boundary.
6. A wireless router transmits at 2.4 GHz. Find the wavelength in a vacuum, taking c = 3.00 × 10⁸ m s⁻¹.
7. A radio pulse from a lunar orbiter is received 3.9 × 10⁸ m away. Find the travel time.
8. Sound, microwaves, ultrasound and X-rays. Which can be plane-polarised?
9. State the direction of the oscillation of air particles in a sound wave relative to the direction of travel.
10. A transmitting aerial is horizontal. How should the receiving rod aerial be oriented for the strongest signal, and what happens at 90° to this?

Answers

1. f = 1/0.025 = 40 Hz.
2. c = fλ = 1200 × 0.28 = 336 m s⁻¹.
3. 0.45/0.60 = 0.75 cycle: 270°, or 3π/2 rad (4.71 rad).
4. 6.0/16 = 0.375 cycle: 135°, or 3π/4 rad (2.36 rad).
5. d = 1540 × 68 × 10⁻⁶ / 2 = 0.052 m (5.2 cm).
6. λ = c/f = 3.00 × 10⁸ / 2.4 × 10⁹ = 0.125 m.
7. t = d/c = 3.9 × 10⁸ / 3.00 × 10⁸ = 1.3 s.
8. Microwaves and X-rays (transverse). Sound and ultrasound are longitudinal.
9. Parallel to the direction of travel (along the same line).
10. Horizontal, parallel to the transmitter. At 90° the signal is close to zero, because the rod is at right angles to the electric field oscillation.

Where marks are usually lost

• Writing that the particles “move along with the wave” instead of oscillating about fixed positions.
• Defining wavelength as “the length of a wave” without saying it is the distance between adjacent points in phase.
• Using the whole separation without dividing by λ, or forgetting to say which way round a phase difference goes.
• Mixing up the graphs: reading T from a displacement-distance graph.
• Leaving out the factor of 2 in ultrasound depth calculations.
• Not converting MHz, GHz, μs or nm before substituting.
• Saying polarisation shows light is “a wave” rather than a transverse wave.
• Describing a longitudinal wave with a drawing of crests and troughs. Use compressions and rarefactions.
• Describing polarisation without mentioning the transmission axis or the direction of oscillation.

Next steps

Work through the practice questions, re-read the study guide where you slipped, and take a free 10-minute check on the diagnostics page.

Official syllabus

OxfordAQA International AS and A-level Physics (9630), Version 4.4, for International AS and A-level exams May/June 2020 onwards, published by OxfordAQA. Sections 3.5.3 and 3.5.4.