Progressive waves — AQA A-Level Physics

Progressive waves are fundamental to understanding how energy is transferred through space and matter. This topic covers the definitions of transverse and longitudinal waves, the key wave properties (amplitude, wavelength, frequency, period, phase, and wave speed), and the wave equation v = f lambda. You will also learn to interpret displacement-distance and displacement-time graphs, and to calculate phase differences.

This topic is essential for later study of wave behaviour such as reflection, refraction, diffraction, interference, and stationary waves. It also underpins many real-world applications, from medical ultrasound to communication technologies. A strong grasp of progressive waves is crucial for success in AQA A-Level Physics Paper 1 and beyond.

• →A progressive wave transfers energy without transferring matter; oscillations are either transverse (perpendicular to energy transfer) or longitudinal (parallel to energy transfer).
• →Key wave quantities: amplitude (maximum displacement), wavelength (distance between successive identical points), frequency (oscillations per second), period (time for one oscillation), and wave speed (distance travelled per second).
• →The wave equation v = f lambda relates wave speed, frequency, and wavelength; for a given medium, wave speed is typically constant, so frequency and wavelength are inversely proportional.
• →Phase difference describes the fraction of a cycle between two points on a wave, measured in radians or degrees; it can be calculated from path difference using phi = (2 pi / lambda) x path difference.
• →Displacement-distance graphs show the wave profile at a given instant, while displacement-time graphs show the oscillation of a single point over time; both are sinusoidal for simple harmonic waves.

• States that particles oscillate about equilibrium positions and that energy, not the particles, is transferred along the wave.
• Defines amplitude as maximum displacement from equilibrium and wavelength as distance between successive points in phase.
• Defines frequency as oscillations per second and period as the time for one complete oscillation, using f = 1/T.
• Applies c = f λ correctly, including unit consistency, to find speed, frequency or wavelength.
• Describes phase difference as a fraction of a cycle and converts between fractions, degrees and radians, e.g. one quarter cycle = 90° = π/2 rad.

• 💡Write the wave equation as c = f λ and substitute values with units before calculating.
• 💡When asked for phase difference, state the unit clearly, choosing radians, degrees or a fraction of a cycle as requested.
• 💡Sketch or annotate a displacement–distance graph to show amplitude and wavelength before using them in calculations.
• 💡Always define the direction of oscillation relative to energy transfer when distinguishing transverse and longitudinal waves. Use the words 'perpendicular' and 'parallel' explicitly.
• 💡When using the wave equation, write it down first, substitute values with units, and round your final answer appropriately. Check that your answer has the correct unit and is in SI units.
• 💡For phase difference calculations, remember that a path difference of one wavelength corresponds to a phase difference of 2 pi radians (360 degrees). Use the formula phi = (2 pi / lambda) x path difference.

• Treating particles as travelling with the wave; the correction is that particles oscillate about fixed equilibrium positions while the wave pattern and energy advance.
• Confusing period with frequency; the correction is that period is the time for one cycle and frequency is the reciprocal of period.
• Measuring wavelength between a crest and the next trough; the correction is to measure between successive crests, successive troughs or any two successive points in phase.
• Students often think that particles travel along with the wave. In fact, particles oscillate about a fixed equilibrium position, and only energy is transferred.
• Many confuse frequency with period. Frequency is the number of oscillations per second (Hz), while period is the time for one complete oscillation (s); they are reciprocals: T = 1/f.
• Some believe that increasing frequency always increases wave speed. In a given medium, wave speed is usually constant, so increasing frequency decreases wavelength proportionally.

1. 1Day 1-2: Learn definitions of key terms (amplitude, wavelength, frequency, period, phase, wave speed) and distinguish between transverse and longitudinal waves with examples.
2. 2Day 3-4: Master the wave equation v = f lambda and practice calculations, including unit conversions and rearranging the formula.
3. 3Day 5-6: Study displacement-distance and displacement-time graphs; practice interpreting them and determining wave properties from graphs.
4. 4Day 7-8: Learn to calculate phase difference using path difference and the formula phi = (2 pi / lambda) x path difference; practice with different scenarios.
5. 5Day 9-10: Attempt past paper questions on progressive waves, focusing on exam technique and common pitfalls; review mark schemes carefully.

• 📋Multiple-choice questions testing definitions and basic properties of transverse and longitudinal waves. Advice: read all options carefully and eliminate incorrect ones based on precise definitions.
• 📋Calculations using v = f lambda, often requiring unit conversions or rearranging the equation. Advice: always show your working and include units in your final answer.
• 📋Graph interpretation questions where you must determine amplitude, wavelength, period, or frequency from displacement-distance or displacement-time graphs. Advice: check the axes labels and units carefully; remember that displacement-distance graphs give wavelength, while displacement-time graphs give period.
• 📋Phase difference calculations, either directly from a graph or using path difference. Advice: use the formula phi = (2 pi / lambda) x path difference and express your answer in radians or degrees as requested.