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    Progressive waves — AQA A-Level Physics

    Teaching note checked against the official specification.

    A progressive wave is a disturbance that transfers energy through a medium or vacuum without transferring matter, characterised by oscillations of particles or fields. In AQA A-Level Physics, you must describe waves using displacement, amplitude, wavelength, frequency, period, phase and wave speed, and apply the wave equation v = f lambda to solve problems.

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    Progressive waves explained

    A progressive wave transfers energy through a medium as particles oscillate about fixed equilibrium positions; the wave pattern travels while the particles themselves do not travel with it.

    Read the full explanation

    Amplitude is the maximum displacement from equilibrium, frequency f is oscillations per second, wavelength λ is the distance between successive points in phase, and speed c is how fast a crest advances. Phase describes where a particle sits within its cycle; phase difference compares two points, measured in radians, degrees or fractions of a cycle. The wave equation c = f λ links speed, frequency and wavelength, and f = 1/T links frequency to period. For example, a wave of frequency 50 Hz and wavelength 0.40 m travels at c = 50 × 0.40 = 20 m s⁻¹.

    Read the Progressive waves study guideFull revision notes for AQA A-Level Physics

    Your focus

    1. Describe particle oscillation and energy transfer in a progressive wave.
    2. Define amplitude, frequency, wavelength, speed, phase and phase difference.
    3. Use c = f λ and f = 1/T to solve wave problems, including phase difference expressed in radians, degrees or fractions of a cycle.

    Which command word is this?

    Give a precise, formal statement of the meaning of a term. For example, 'Define wavelength' requires: 'The distance between two successive points in phase on a wave' or 'the distance between two successive peaks/troughs'.

    Progressive waves exam tips

    Topic Overview

    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.

    Key Concepts
    • →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.
    Marking Points
    • 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.
    Examiner Tips
    • 💡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.
    Common Mistakes
    • 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.
    Revision Plan
    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.
    Exam Question Types
    • 📋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.
    Command Word Expectations (AQA)
    Define

    Give a precise, formal statement of the meaning of a term. For example, 'Define wavelength' requires: 'The distance between two successive points in phase on a wave' or 'the distance between two successive peaks/troughs'.

    Calculate

    Use the given data and appropriate equations to find a numerical answer. You must show your working, include units, and round to an appropriate number of significant figures. For example, 'Calculate the wave speed' requires substitution into v = f lambda and a final answer with unit m/s.

    Explain

    Give reasons or mechanisms to justify a statement. For example, 'Explain why the wave is longitudinal' requires stating that the oscillations are parallel to the direction of energy transfer, and possibly giving an example like sound.

    How Students Lose Marks (Examiner Pitfalls)
    Pitfall: Students often confuse transverse and longitudinal waves, or incorrectly state that particles travel with the wave. They also forget that in a longitudinal wave, particle displacement is parallel to the direction of energy transfer, not perpendicular.
    ❌ Weak Answer (Loses Marks):A transverse wave moves particles up and down while the wave goes forward. A longitudinal wave moves particles side to side.
    Example improved answer:In a transverse wave, the oscillations of particles (or fields) are perpendicular to the direction of energy transfer, e.g. electromagnetic waves or waves on a string. In a longitudinal wave, the oscillations are parallel to the direction of energy transfer, producing compressions and rarefactions, e.g. sound waves. In both cases, energy is transferred without net transfer of matter.
    Examiner Tip: Always state the direction of oscillation relative to energy transfer. Use the terms 'perpendicular' and 'parallel' explicitly, and give a named example for each type.
    Pitfall: When using the wave equation v = f lambda, students frequently mix up frequency and period, or forget to convert units (e.g. cm to m, kHz to Hz). They also assume wave speed changes with frequency in the same medium, which is only true for dispersive waves.
    ❌ Weak Answer (Loses Marks):v = f x lambda = 50 x 2 = 100 m/s. So the wave speed is 100 m/s.
    Example improved answer:Given frequency f = 50 Hz and wavelength lambda = 2.0 m, using v = f lambda gives v = 50 x 2.0 = 100 m/s. The wave speed is 100 m/s. Note that for a given medium, wave speed is generally constant, so if frequency increases, wavelength decreases proportionally.
    Examiner Tip: Always write the formula, substitute values with units, and give the final answer with the correct unit. Check that all quantities are in SI units before calculating.
    Step-by-Step Worked Solutions

    Question: A progressive wave has a frequency of 250 Hz and a wavelength of 1.2 m. Calculate the speed of the wave and the period of oscillation.

    1. 1.Step 1: Identify given values: frequency f = 250 Hz, wavelength lambda = 1.2 m.
    2. 2.Step 2: Use the wave equation v = f lambda. Substitute: v = 250 x 1.2 = 300 m/s.
    3. 3.Step 3: Calculate period T using T = 1/f. T = 1/250 = 0.004 s (or 4 ms).
    4. 4.Step 4: State final answers with units: speed = 300 m/s, period = 0.004 s.
    Final Answer: Wave speed = 300 m/s; period = 0.004 s.

    Question: A graph of displacement against distance for a progressive wave shows a sinusoidal shape with a maximum displacement of 0.05 m and a distance between successive peaks of 0.8 m. The wave travels at 4.0 m/s. Determine the frequency and the phase difference between two points 0.2 m apart.

    1. 1.Step 1: From the graph, amplitude A = 0.05 m and wavelength lambda = 0.8 m.
    2. 2.Step 2: Use v = f lambda to find frequency: f = v / lambda = 4.0 / 0.8 = 5.0 Hz.
    3. 3.Step 3: Phase difference phi = (2 pi / lambda) x path difference. Path difference = 0.2 m.
    4. 4.Step 4: phi = (2 pi / 0.8) x 0.2 = (2 pi) x 0.25 = pi/2 radians (or 90 degrees).
    Final Answer: Frequency = 5.0 Hz; phase difference = pi/2 radians (90 degrees).
    Active Recall Memory Test
    What is the difference between a transverse and a longitudinal wave?
    Key Fact: In a transverse wave, oscillations are perpendicular to the direction of energy transfer (e.g., light). In a longitudinal wave, oscillations are parallel to the direction of energy transfer (e.g., sound).
    State the wave equation and define each symbol.
    Key Fact: v = f lambda, where v is wave speed (m/s), f is frequency (Hz), and lambda is wavelength (m).
    How is phase difference related to path difference?
    Key Fact: Phase difference (in radians) = (2 pi / lambda) x path difference. A path difference of one wavelength corresponds to a phase difference of 2 pi radians (360 degrees).
    What is the period of a wave with frequency 50 Hz?
    Key Fact: Period T = 1/f = 1/50 = 0.02 s (or 20 ms).
    Frequently Asked Questions
    What is a progressive wave in AQA A-Level Physics?
    A progressive wave is a wave that transfers energy from one place to another without transferring matter. It is characterised by oscillations of particles or fields, and can be transverse or longitudinal. In AQA A-Level Physics, you need to describe progressive waves using quantities such as amplitude, wavelength, frequency, period, and wave speed, and apply the wave equation v = f lambda.
    How do you calculate wave speed using frequency and wavelength?
    Wave speed (v) is calculated using the equation v = f lambda, where f is frequency in hertz (Hz) and lambda is wavelength in metres (m). For example, if a wave has a frequency of 200 Hz and a wavelength of 1.5 m, its speed is 200 x 1.5 = 300 m/s. Always ensure units are in SI before calculating.
    What is the difference between displacement-distance and displacement-time graphs?
    A displacement-distance graph shows the displacement of all points on a wave at a single instant in time; the distance between successive peaks gives the wavelength. A displacement-time graph shows the displacement of a single point on the wave over time; the time between successive peaks gives the period. Both are sinusoidal for simple harmonic waves.
    How do you calculate phase difference between two points on a wave?
    Phase difference (phi) in radians is calculated using phi = (2 pi / lambda) x path difference, where path difference is the distance between the two points and lambda is the wavelength. For example, if the path difference is half a wavelength, the phase difference is pi radians (180 degrees). You can also express phase difference in degrees by using 360 degrees instead of 2 pi.
    Why does wave speed remain constant when frequency changes in a given medium?
    In a given medium, the speed of a wave is determined by the properties of the medium (e.g., tension and mass per unit length for a string, or density and elasticity for sound). When frequency increases, the wavelength decreases proportionally so that the product f lambda remains constant. This is why wave speed does not change with frequency in a non-dispersive medium.
    What are common mistakes students make with progressive waves in exams?
    Common mistakes include confusing transverse and longitudinal waves, forgetting to convert units (e.g., cm to m), mixing up frequency and period, and incorrectly calculating phase difference. Students also often assume particles travel with the wave, or that wave speed changes with frequency in the same medium. Always double-check definitions and use the correct formula with consistent units.