Transverse and longitudinal waves Revision Notes

    Subject: Physics | Level: GCSE | Exam Board: OCR

    Waves are the mechanism by which energy is transferred across space and matter, and this topic sits at the heart of OCR GCSE Physics. Candidates must master the precise distinction between transverse and longitudinal waves, command the wave equation v = fλ with confidence, and interpret both displacement-distance and displacement-time graphs accurately. Examiners consistently award marks for exact language — particularly the terms 'perpendicular', 'parallel', 'compression', and 'rarefaction' — making this a topic where precision of expression is as important as conceptual understanding.

    Revision Notes & Key Concepts

    ![Transverse and Longitudinal Waves — OCR GCSE Physics Topic 4.1](https://xnnrgnazirrqvdgfhvou.supabase.co/storage/v1/object/public/study-guide-assets/guide_442c8941-de33-44ec-9057-abfe612ce957/header_image.png) ## Overview Waves are one of the most pervasive phenomena in the physical universe, and OCR GCSE Physics dedicates a substantial portion of Topic 4 to ensuring candidates understand them with rigour. At its core, this topic asks a deceptively simple question: how does energy travel from one place to another? The answer — through wave motion — underpins everything from the warmth of sunlight to the sound of music, from the diagnosis of broken bones via ultrasound to the detection of earthquakes thousands of kilometres away. For the OCR specification, candidates are assessed on two principal wave types — transverse and longitudinal — and on the quantitative relationship between wave speed, frequency, and wavelength. The topic also encompasses the required practical PAG P8, in which candidates investigate wave properties using a ripple tank or vibration transducer. Exam questions on this topic range from 1-mark definition recalls to 6-mark extended responses describing experimental methods. Assessment Objective 1 (knowledge recall) accounts for 40% of marks, AO2 (application) for 40%, and AO3 (analysis and evaluation) for 20%, meaning candidates must be equally comfortable defining terms, performing calculations, and critically evaluating experimental data. This topic connects synoptically to the electromagnetic spectrum (Topic 4.2), sound and ultrasound (Topic 4.3), seismic waves (Topic 4.5), and the properties of light including reflection and refraction (Topic 4.4). Mastery here creates a strong foundation for the entire waves section of the specification. ![Wave Properties: Key Measurements — displacement-distance and displacement-time graphs compared](https://xnnrgnazirrqvdgfhvou.supabase.co/storage/v1/object/public/study-guide-assets/guide_442c8941-de33-44ec-9057-abfe612ce957/wave_properties_diagram.png) ## Key Concepts ### Concept 1: What All Waves Have in Common Before distinguishing between wave types, it is essential to understand what all waves share. Every wave transfers energy from one location to another without the permanent bulk transfer of matter. This is a fundamental principle: the particles or fields through which a wave travels oscillate about their equilibrium positions, but they do not travel with the wave. The analogy of a Mexican wave in a stadium is instructive — spectators (particles) move up and down, but the wave pattern travels around the ground. All waves are characterised by four measurable properties. **Wavelength (λ)** is the distance between two consecutive corresponding points on a wave — for instance, from one crest to the next, or from one compression to the next. It is measured in metres (m). **Amplitude (A)** is the maximum displacement of a particle from its equilibrium (rest) position, also measured in metres. A larger amplitude indicates greater energy being transferred. **Frequency (f)** is the number of complete wave cycles passing a fixed point per second, measured in Hertz (Hz). **Period (T)** is the time taken for one complete wave cycle to pass a fixed point, measured in seconds (s). Period and frequency are reciprocals: T = 1/f. A critical examination skill is distinguishing between a **displacement-distance graph** and a **displacement-time graph**. Both produce an identical sinusoidal shape, but they measure fundamentally different things. The displacement-distance graph allows candidates to read off the **wavelength** directly from the x-axis. The displacement-time graph allows candidates to read off the **period** from the x-axis. Confusing these two graphs is one of the most frequently penalised errors at GCSE level. ### Concept 2: Transverse Waves In a **transverse wave**, the oscillations of the particles (or fields) are **perpendicular** — at 90 degrees — to the direction of energy transfer. This is the mark-scheme definition, and candidates must use the word 'perpendicular' or state '90 degrees' explicitly to earn the mark. Saying that 'the wave moves at right angles to the vibration' is acceptable, but stating that 'the wave moves perpendicular to itself' is not — the reference must be to the direction of energy transfer. Examples of transverse waves include all electromagnetic waves (light, radio waves, X-rays, microwaves, infrared, ultraviolet, and gamma rays) and water surface waves. In electromagnetic waves, it is the oscillating electric and magnetic fields that are perpendicular to the direction of travel — there is no physical medium required. Water surface waves are modelled as transverse at GCSE, with the water surface moving vertically while wave energy travels horizontally. On a diagram, a transverse wave appears as a sinusoidal curve. The highest points are **crests** and the lowest points are **troughs**. The amplitude is measured from the equilibrium line to a crest (or trough). The wavelength spans from one crest to the next, or equivalently from any point to the next corresponding point in the cycle. ### Concept 3: Longitudinal Waves In a **longitudinal wave**, the oscillations of the particles are **parallel** to the direction of energy transfer — they vibrate back and forth along the same line as the wave travels. The essential mnemonic here is: **'Longitudinal is Along'**. This single phrase encodes the parallel relationship and has helped countless candidates secure definition marks. The primary example of a longitudinal wave is **sound**. When a loudspeaker cone vibrates, it pushes air molecules back and forth in the direction the sound is travelling. This creates alternating regions of high and low pressure that propagate outward from the source. ![Longitudinal Wave: Sound — compressions, rarefactions, and the pressure-distance relationship](https://xnnrgnazirrqvdgfhvou.supabase.co/storage/v1/object/public/study-guide-assets/guide_442c8941-de33-44ec-9057-abfe612ce957/longitudinal_wave_diagram.png) These alternating regions are called **compressions** and **rarefactions**. A **compression** is a region where particles are closer together than their normal spacing, resulting in **high pressure and high density**. A **rarefaction** is a region where particles are further apart than normal, resulting in **low pressure and low density**. Candidates must include both the pressure and the density description for full marks — stating only 'high pressure' for a compression may not attract credit if the mark scheme requires density to be mentioned. The wavelength of a longitudinal wave is measured from one compression to the next compression (or from one rarefaction to the next rarefaction) — the distance between two consecutive corresponding points, exactly as with transverse waves. ### Concept 4: The Wave Equation The wave equation is the single most important quantitative relationship in this topic: **v = fλ** Where v is wave speed in metres per second (m/s), f is frequency in Hertz (Hz), and λ is wavelength in metres (m). This equation is **not provided on the OCR formula sheet** and must be memorised. ![The Wave Equation v = fλ and PAG P8: Ripple Tank Practical](https://xnnrgnazirrqvdgfhvou.supabase.co/storage/v1/object/public/study-guide-assets/guide_442c8941-de33-44ec-9057-abfe612ce957/wave_equation_ripple_tank.png) The examiner's recommended method for applying this equation is a strict three-step process. First, write down the equation in its standard form. Second, substitute the known values with their units. Third, rearrange and calculate. This approach secures method marks even if the arithmetic is incorrect, because OCR mark schemes award a mark for correct substitution prior to any rearrangement. Unit conversion is a critical skill here. Frequency may be given in kilohertz (kHz) — multiply by 1,000 to convert to Hz. Wavelength may be given in centimetres (cm) — divide by 100 to convert to metres. Failing to convert units before substituting is the single most common source of power-of-ten errors in wave calculations. ## Mathematical Relationships | Equation | Variables | Formula Sheet? | Notes | |---|---|---|---| | v = fλ | v (m/s), f (Hz), λ (m) | **Must memorise** | Core wave equation | | T = 1/f | T (s), f (Hz) | **Must memorise** | Period-frequency relationship | | f = 1/T | f (Hz), T (s) | **Must memorise** | Frequency from period | **Unit Conversion Reference:** | Given Unit | Convert To | Operation | |---|---|---| | kHz (kilohertz) | Hz | × 1,000 | | MHz (megahertz) | Hz | × 1,000,000 | | cm (centimetres) | m | ÷ 100 | | mm (millimetres) | m | ÷ 1,000 | | nm (nanometres) | m | ÷ 1,000,000,000 | ## Practical Applications and Required Practical (PAG P8) The OCR required practical for this topic is **PAG P8: Investigating Waves**. Candidates may be assessed on this in the written examination, and 6-mark questions describing the method are common. **Apparatus:** Ripple tank, vibration transducer (dipper), signal generator, strobe light, metre ruler, stopwatch, white paper or screen beneath the tank. **Method:** Fill the ripple tank with a shallow, uniform depth of water. Connect the vibration transducer to the signal generator and set a known frequency. Use the strobe light to 'freeze' the wavefronts by matching the strobe frequency to the wave frequency. Measure the distance across multiple wavelengths using a metre ruler, then divide by the number of wavelengths to calculate the mean wavelength. This reduces percentage uncertainty. Record the frequency from the signal generator display. Calculate wave speed using v = fλ. **Key Examiner Expectations for 6-mark Questions:** Name specific instruments (strobe light, metre ruler, signal generator). Explain how uncertainty is reduced (measuring multiple wavelengths and finding the mean). State what is measured and how. Describe a safety consideration if relevant (e.g., electrical equipment near water — keep signal generator away from the tank). **Graph/Data Skills:** When plotting wave data, candidates should be able to plot wavelength against 1/frequency and recognise that the gradient of this graph equals the wave speed. They should also be able to read wavelength from a displacement-distance graph by identifying the distance between two consecutive crests or troughs, and read period from a displacement-time graph by identifying the time for one complete cycle.

    Revision Podcast Transcript

    PODCAST SCRIPT: Transverse and Longitudinal Waves — OCR GCSE Physics (Topic 4.1) Duration: Approximately 10 minutes Voice: Warm, enthusiastic female educator/tutor --- INTRO (approx. 1 minute) --- Hello and welcome to your OCR GCSE Physics revision podcast. I'm so glad you're here, because today we're diving into one of the most fundamental and fascinating topics in the entire specification — waves. Specifically, we're covering Topic 4.1: Transverse and Longitudinal Waves. Now, I know what some of you might be thinking — 'waves, really? How exciting can that be?' But here's the thing: waves are everywhere. The light hitting your eyes right now, the sound of my voice reaching your ears, the ripples in a puddle after rain — all of these are waves, and understanding them unlocks so much of the rest of your physics course. This topic connects directly to the electromagnetic spectrum, sound, seismic waves, and even medical imaging. Examiners absolutely love linking waves to real-world contexts, so getting this solid is going to pay dividends across the whole paper. By the end of this podcast, you'll be able to define both types of waves with precision, apply the wave equation confidently, and walk into your exam knowing exactly what the mark scheme is looking for. Let's get started. --- CORE CONCEPTS (approx. 5 minutes) --- Let's begin with the big picture. All waves transfer energy from one place to another — and this is crucial — without permanently transferring matter. The particles or fields that make up the wave oscillate, or vibrate, but they don't travel along with the wave. Think of a Mexican wave in a football stadium. The people stand up and sit down — they oscillate — but they don't actually move around the stadium. The wave, the pattern of movement, travels around. That's exactly what's happening in physics waves too. Now, there are two fundamental types of wave, and the difference between them comes down to one key question: in which direction do the particles oscillate relative to the direction the wave is travelling? Let's start with TRANSVERSE waves. In a transverse wave, the oscillations of the particles are perpendicular — that means at 90 degrees — to the direction of energy transfer. Say that again with me: perpendicular to the direction of energy transfer. This is the definition the mark scheme is looking for, and it's worth one mark every single time it appears. A brilliant example of a transverse wave is light, or any electromagnetic wave. When light travels horizontally, the electric and magnetic fields oscillate up and down, or side to side — perpendicular to the direction of travel. Water surface waves are also modelled as transverse waves at GCSE — the water surface moves up and down while the wave energy travels horizontally across the surface. If you draw a transverse wave on paper, you get that classic sinusoidal S-curve — peaks going up, troughs going down, with the wave moving left to right along the page. This is a displacement-distance graph, and it's incredibly useful for reading off key measurements, which we'll come to in a moment. Now let's talk about LONGITUDINAL waves. In a longitudinal wave, the oscillations of the particles are parallel to the direction of energy transfer. Parallel — meaning along the same line, in the same direction. The key mnemonic here is: Longitudinal is Along. Say it: Longitudinal is Along. That one phrase will save you marks in the exam. The classic example of a longitudinal wave is sound. When a loudspeaker vibrates, it pushes air particles back and forth in the same direction that the sound is travelling. This creates alternating regions of high pressure — called compressions — where the particles are bunched closely together, and regions of low pressure — called rarefactions — where the particles are spread further apart. Examiners love asking about compressions and rarefactions, so let's be really precise. A compression is a region of high pressure and high density, where particles are closer together than their normal spacing. A rarefaction is a region of low pressure and low density, where particles are further apart than their normal spacing. You need both the pressure AND the density description for full marks — just saying 'high pressure' on its own might not be enough. Now let's move on to the key measurements that apply to ALL waves, whether transverse or longitudinal. WAVELENGTH, represented by the Greek letter lambda, is the distance between two consecutive corresponding points on a wave — for example, from one crest to the next crest, or from one compression to the next compression. The key word is 'corresponding' — the points must be at the same position in their cycle. Wavelength is measured in metres. AMPLITUDE is the maximum displacement of a particle from its equilibrium position. On a transverse wave diagram, it's the height from the middle line to the peak. Amplitude is related to the energy carried by the wave — a larger amplitude means more energy. Amplitude is also measured in metres. FREQUENCY is the number of complete waves passing a point per second. It's measured in Hertz, abbreviated Hz. One hertz means one complete wave per second. You'll also encounter kilohertz — that's kHz — which is one thousand hertz, and megahertz — MHz — which is one million hertz. Watch out for unit conversions here — this is one of the most common sources of power-of-ten errors in the exam. PERIOD, represented by the letter T, is the time taken for one complete wave to pass a point. Period and frequency are reciprocals of each other: T equals one over f, and f equals one over T. Period is measured in seconds. Now, the most important equation in this topic — and one you absolutely must memorise because it is NOT given on the OCR formula sheet — is the wave equation: v equals f times lambda. v is the wave speed in metres per second. f is the frequency in hertz. lambda is the wavelength in metres. This equation tells us that the speed of a wave equals its frequency multiplied by its wavelength. The examiner's golden rule for using this equation is: write it down first, then substitute your values in, then rearrange if needed. This three-step approach guarantees you method marks even if you make an arithmetic error at the end. Let me give you a quick example. A sound wave has a frequency of 440 hertz and a wavelength of 0.75 metres. What is its speed? Step one: write v equals f lambda. Step two: substitute — v equals 440 times 0.75. Step three: calculate — v equals 330 metres per second. Clean, clear, full marks. --- EXAM TIPS AND COMMON MISTAKES (approx. 2 minutes) --- Right, let's talk about the mistakes that cost students marks every single year — and how you're going to avoid every single one of them. Mistake number one: imprecise definitions. When asked to define a transverse wave, many candidates write something like 'the wave moves perpendicular to the vibration.' This is actually backwards and will not earn the mark. The correct phrasing is: 'the oscillations are perpendicular to the direction of energy transfer.' The oscillations are what's perpendicular — not the wave movement. Get this the right way round. Mistake number two: confusing displacement-time graphs with displacement-distance graphs. A displacement-TIME graph shows you the PERIOD — the time for one complete cycle. A displacement-DISTANCE graph shows you the WAVELENGTH — the distance for one complete cycle. These look identical on paper, so always check the axis labels before reading off any value. Candidates who read wavelength from a time graph, or period from a distance graph, lose marks every year. Mistake number three: unit conversion errors. If a frequency is given in kilohertz, you must convert to hertz before substituting into v equals f lambda. Multiply by 1000. If a wavelength is given in centimetres, convert to metres by dividing by 100. Always check your units before calculating. Mistake number four: describing water waves as longitudinal. Water surface waves are transverse at GCSE level. Sound waves are longitudinal. Don't mix these up. Now, for 6-mark extended response questions about the ripple tank practical — PAG P8 — examiners want you to name specific measuring instruments and explain how they reduce uncertainty. Don't just say 'measure the wavelength with a ruler.' Say: 'use a metre ruler to measure the distance across multiple wavelengths, then divide by the number of wavelengths to find the mean wavelength — this reduces the percentage uncertainty in the measurement.' That level of detail is what separates a 5 from a 6. For command words: 'State' or 'Give' wants a brief factual answer — one or two words or a short phrase. 'Describe' wants you to say what something is like, using correct terminology. 'Explain' wants you to say WHY — use the word 'because' to link cause and effect. 'Calculate' means show your working, state the formula, substitute values, and include units in your final answer. --- QUICK-FIRE RECALL QUIZ (approx. 1 minute) --- Right, let's test your recall. I'll ask a question, pause for a few seconds, then give the answer. No peeking at your notes! Question one: In a transverse wave, the oscillations are in which direction relative to energy transfer? [pause] Perpendicular — at 90 degrees. Question two: What is the mnemonic for remembering longitudinal waves? [pause] Longitudinal is Along. Question three: What are the two regions of a longitudinal wave called? [pause] Compressions and rarefactions. Question four: Write down the wave equation. [pause] v equals f lambda. Question five: A wave has frequency 50 Hz and wavelength 6 metres. What is its speed? [pause] 300 metres per second. Question six: Which graph type shows you the wavelength — displacement-time or displacement-distance? [pause] Displacement-distance. How did you do? If you got all six, you're in great shape. If you stumbled on any, go back and review that section. --- SUMMARY AND SIGN-OFF (approx. 1 minute) --- Let's bring it all together. The two types of wave are transverse — oscillations perpendicular to energy transfer, like light and water waves — and longitudinal — oscillations parallel to energy transfer, like sound waves. All waves have wavelength, amplitude, frequency, and period. The wave equation v equals f lambda links speed, frequency, and wavelength, and you must memorise it. In the exam, always write the equation first, substitute values second, rearrange third. Watch out for unit conversions, and never confuse your displacement-time graph with your displacement-distance graph. You've got this. Waves are one of those topics that, once it clicks, it really clicks — and I hope today's session has helped it click for you. Keep practising those calculations, keep testing yourself on those definitions, and remember: every mark you understand is a mark you can earn. Good luck with your revision, and I'll see you in the next episode. Take care!

    Key Terms & Definitions

    Transverse wave
    A wave in which the oscillations of the particles (or fields) are perpendicular (at 90°) to the direction of energy transfer.
    Longitudinal wave
    A wave in which the oscillations of the particles are parallel to the direction of energy transfer.
    Wavelength (λ)
    The distance between two consecutive corresponding points on a wave — for example, from one crest to the next crest, or from one compression to the next compression. Measured in metres (m).
    Amplitude (A)
    The maximum displacement of a particle from its equilibrium (rest) position. Measured in metres (m). A larger amplitude indicates greater energy transfer.
    Frequency (f)
    The number of complete wave cycles passing a fixed point per second. Measured in Hertz (Hz), where 1 Hz = 1 complete wave per second.
    Period (T)
    The time taken for one complete wave cycle to pass a fixed point. Measured in seconds (s). Related to frequency by T = 1/f.
    Compression
    A region in a longitudinal wave where particles are closer together than their equilibrium spacing, resulting in a region of high pressure and high density.
    Rarefaction
    A region in a longitudinal wave where particles are further apart than their equilibrium spacing, resulting in a region of low pressure and low density.
    Wave speed (v)
    The distance travelled by a wave per unit time, measured in metres per second (m/s). Related to frequency and wavelength by v = fλ.

    Worked Examples

    Practice Questions

    Transverse and longitudinal waves

    OCR
    GCSE
    Physics

    Waves are the mechanism by which energy is transferred across space and matter, and this topic sits at the heart of OCR GCSE Physics. Candidates must master the precise distinction between transverse and longitudinal waves, command the wave equation v = fλ with confidence, and interpret both displacement-distance and displacement-time graphs accurately. Examiners consistently award marks for exact language — particularly the terms 'perpendicular', 'parallel', 'compression', and 'rarefaction' — making this a topic where precision of expression is as important as conceptual understanding.

    9
    Min Read
    5
    Examples
    6
    Questions
    9
    Key Terms
    🎙 Podcast Episode
    Transverse and longitudinal waves
    0:00-0:00

    Study Notes

    Transverse and Longitudinal Waves — OCR GCSE Physics Topic 4.1

    Overview

    Waves are one of the most pervasive phenomena in the physical universe, and OCR GCSE Physics dedicates a substantial portion of Topic 4 to ensuring candidates understand them with rigour. At its core, this topic asks a deceptively simple question: how does energy travel from one place to another? The answer — through wave motion — underpins everything from the warmth of sunlight to the sound of music, from the diagnosis of broken bones via ultrasound to the detection of earthquakes thousands of kilometres away.

    For the OCR specification, candidates are assessed on two principal wave types — transverse and longitudinal — and on the quantitative relationship between wave speed, frequency, and wavelength. The topic also encompasses the required practical PAG P8, in which candidates investigate wave properties using a ripple tank or vibration transducer. Exam questions on this topic range from 1-mark definition recalls to 6-mark extended responses describing experimental methods. Assessment Objective 1 (knowledge recall) accounts for 40% of marks, AO2 (application) for 40%, and AO3 (analysis and evaluation) for 20%, meaning candidates must be equally comfortable defining terms, performing calculations, and critically evaluating experimental data.

    This topic connects synoptically to the electromagnetic spectrum (Topic 4.2), sound and ultrasound (Topic 4.3), seismic waves (Topic 4.5), and the properties of light including reflection and refraction (Topic 4.4). Mastery here creates a strong foundation for the entire waves section of the specification.

    Wave Properties: Key Measurements — displacement-distance and displacement-time graphs compared

    Key Concepts

    Concept 1: What All Waves Have in Common

    Before distinguishing between wave types, it is essential to understand what all waves share. Every wave transfers energy from one location to another without the permanent bulk transfer of matter. This is a fundamental principle: the particles or fields through which a wave travels oscillate about their equilibrium positions, but they do not travel with the wave. The analogy of a Mexican wave in a stadium is instructive — spectators (particles) move up and down, but the wave pattern travels around the ground.

    All waves are characterised by four measurable properties. Wavelength (λ) is the distance between two consecutive corresponding points on a wave — for instance, from one crest to the next, or from one compression to the next. It is measured in metres (m). Amplitude (A) is the maximum displacement of a particle from its equilibrium (rest) position, also measured in metres. A larger amplitude indicates greater energy being transferred. Frequency (f) is the number of complete wave cycles passing a fixed point per second, measured in Hertz (Hz). Period (T) is the time taken for one complete wave cycle to pass a fixed point, measured in seconds (s). Period and frequency are reciprocals: T = 1/f.

    A critical examination skill is distinguishing between a displacement-distance graph and a displacement-time graph. Both produce an identical sinusoidal shape, but they measure fundamentally different things. The displacement-distance graph allows candidates to read off the wavelength directly from the x-axis. The displacement-time graph allows candidates to read off the period from the x-axis. Confusing these two graphs is one of the most frequently penalised errors at GCSE level.

    Concept 2: Transverse Waves

    In a transverse wave, the oscillations of the particles (or fields) are perpendicular — at 90 degrees — to the direction of energy transfer. This is the mark-scheme definition, and candidates must use the word 'perpendicular' or state '90 degrees' explicitly to earn the mark. Saying that 'the wave moves at right angles to the vibration' is acceptable, but stating that 'the wave moves perpendicular to itself' is not — the reference must be to the direction of energy transfer.

    Examples of transverse waves include all electromagnetic waves (light, radio waves, X-rays, microwaves, infrared, ultraviolet, and gamma rays) and water surface waves. In electromagnetic waves, it is the oscillating electric and magnetic fields that are perpendicular to the direction of travel — there is no physical medium required. Water surface waves are modelled as transverse at GCSE, with the water surface moving vertically while wave energy travels horizontally.

    On a diagram, a transverse wave appears as a sinusoidal curve. The highest points are crests and the lowest points are troughs. The amplitude is measured from the equilibrium line to a crest (or trough). The wavelength spans from one crest to the next, or equivalently from any point to the next corresponding point in the cycle.

    Concept 3: Longitudinal Waves

    In a longitudinal wave, the oscillations of the particles are parallel to the direction of energy transfer — they vibrate back and forth along the same line as the wave travels. The essential mnemonic here is: 'Longitudinal is Along'. This single phrase encodes the parallel relationship and has helped countless candidates secure definition marks.

    The primary example of a longitudinal wave is sound. When a loudspeaker cone vibrates, it pushes air molecules back and forth in the direction the sound is travelling. This creates alternating regions of high and low pressure that propagate outward from the source.

    Longitudinal Wave: Sound — compressions, rarefactions, and the pressure-distance relationship

    These alternating regions are called compressions and rarefactions. A compression is a region where particles are closer together than their normal spacing, resulting in high pressure and high density. A rarefaction is a region where particles are further apart than normal, resulting in low pressure and low density. Candidates must include both the pressure and the density description for full marks — stating only 'high pressure' for a compression may not attract credit if the mark scheme requires density to be mentioned.

    The wavelength of a longitudinal wave is measured from one compression to the next compression (or from one rarefaction to the next rarefaction) — the distance between two consecutive corresponding points, exactly as with transverse waves.

    Concept 4: The Wave Equation

    The wave equation is the single most important quantitative relationship in this topic:

    v = fλWhere v is wave speed in metres per second (m/s), f is frequency in Hertz (Hz), and λ is wavelength in metres (m). This equation is not provided on the OCR formula sheet and must be memorised.

    The Wave Equation v = fλ and PAG P8: Ripple Tank Practical

    The examiner's recommended method for applying this equation is a strict three-step process. First, write down the equation in its standard form. Second, substitute the known values with their units. Third, rearrange and calculate. This approach secures method marks even if the arithmetic is incorrect, because OCR mark schemes award a mark for correct substitution prior to any rearrangement.

    Unit conversion is a critical skill here. Frequency may be given in kilohertz (kHz) — multiply by 1,000 to convert to Hz. Wavelength may be given in centimetres (cm) — divide by 100 to convert to metres. Failing to convert units before substituting is the single most common source of power-of-ten errors in wave calculations.

    Mathematical Relationships

    EquationVariablesFormula Sheet?Notes
    v = fλv (m/s), f (Hz), λ (m)Must memoriseCore wave equation
    T = 1/fT (s), f (Hz)Must memorisePeriod-frequency relationship
    f = 1/Tf (Hz), T (s)Must memoriseFrequency from period

    Unit Conversion Reference:

    Given UnitConvert ToOperation
    kHz (kilohertz)Hz× 1,000
    MHz (megahertz)Hz× 1,000,000
    cm (centimetres)m÷ 100
    mm (millimetres)m÷ 1,000
    nm (nanometres)m÷ 1,000,000,000

    Practical Applications and Required Practical (PAG P8)

    The OCR required practical for this topic is PAG P8: Investigating Waves. Candidates may be assessed on this in the written examination, and 6-mark questions describing the method are common.

    Apparatus: Ripple tank, vibration transducer (dipper), signal generator, strobe light, metre ruler, stopwatch, white paper or screen beneath the tank.

    Method: Fill the ripple tank with a shallow, uniform depth of water. Connect the vibration transducer to the signal generator and set a known frequency. Use the strobe light to 'freeze' the wavefronts by matching the strobe frequency to the wave frequency. Measure the distance across multiple wavelengths using a metre ruler, then divide by the number of wavelengths to calculate the mean wavelength. This reduces percentage uncertainty. Record the frequency from the signal generator display. Calculate wave speed using v = fλ.

    Key Examiner Expectations for 6-mark Questions: Name specific instruments (strobe light, metre ruler, signal generator). Explain how uncertainty is reduced (measuring multiple wavelengths and finding the mean). State what is measured and how. Describe a safety consideration if relevant (e.g., electrical equipment near water — keep signal generator away from the tank).

    Graph/Data Skills: When plotting wave data, candidates should be able to plot wavelength against 1/frequency and recognise that the gradient of this graph equals the wave speed. They should also be able to read wavelength from a displacement-distance graph by identifying the distance between two consecutive crests or troughs, and read period from a displacement-time graph by identifying the time for one complete cycle.

    Visual Resources

    3 diagrams and illustrations

    Wave Properties: Key Measurements — displacement-distance and displacement-time graphs compared
    Wave Properties: Key Measurements — displacement-distance and displacement-time graphs compared
    Longitudinal Wave: Sound — compressions, rarefactions, and the pressure-distance relationship
    Longitudinal Wave: Sound — compressions, rarefactions, and the pressure-distance relationship
    The Wave Equation v = fλ and PAG P8: Ripple Tank Practical
    The Wave Equation v = fλ and PAG P8: Ripple Tank Practical

    Interactive Diagrams

    3 interactive diagrams to visualise key concepts

    Decision flowchart for classifying wave types. Starting from the fundamental property shared by all waves, candidates follow the oscillation direction to determine whether a wave is transverse or longitudinal, with examples and key features for each.

    Step-by-step flowchart for solving wave equation calculations. This process guarantees method marks even if the arithmetic is incorrect, because OCR mark schemes award marks for correct equation writing and substitution independently of the final answer.

    Side-by-side comparison map of transverse and longitudinal wave properties. Use this diagram to revise the key differences and check that you can recall examples, oscillation directions, and mnemonics for both wave types.

    Worked Examples

    5 detailed examples with solutions and examiner commentary

    Practice Questions

    Test your understanding — click to reveal model answers

    Q1

    State what is meant by the wavelength of a wave. [1 mark]

    1 marks
    foundation

    Hint: Think about two points on the wave that are in the same position in their cycle.

    Q2

    A water wave has a frequency of 2.5 Hz and a wavelength of 0.40 m. Calculate the speed of the wave. [3 marks]

    3 marks
    foundation

    Hint: Write the wave equation first, then substitute the values. Check your units.

    Q3

    Explain the difference between a compression and a rarefaction in a sound wave. [4 marks]

    4 marks
    standard

    Hint: Think about particle spacing and what this means for pressure and density in each region.

    Q4

    A student measures the speed of sound in air using two microphones connected to a data logger. The student finds that a sound wave has a period of 0.002 s and a wavelength of 0.66 m. (a) Calculate the frequency of the sound wave. [2 marks] (b) Calculate the speed of the sound wave. [2 marks]

    4 marks
    standard

    Hint: For part (a), use the relationship between period and frequency. For part (b), use the wave equation.

    Q5

    A student investigates waves using a ripple tank. Describe how the student could use a ripple tank to measure the speed of water waves. Your answer should include the measurements taken and how the wave speed is calculated. [6 marks]

    6 marks
    challenging

    Hint: Think about what apparatus is needed, what measurements are taken (wavelength and frequency), how uncertainty is reduced, and how wave speed is calculated from these measurements.

    Q6

    A microwave oven uses microwaves with a frequency of 2450 MHz. The speed of microwaves is 3.0 × 10⁸ m/s. Calculate the wavelength of the microwaves. Give your answer in centimetres. [4 marks]

    4 marks
    challenging

    Hint: Convert MHz to Hz first. Rearrange v = fλ for wavelength. Convert your answer from metres to centimetres at the end.

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