Waves: transverse and longitudinal waves, wave properties

What you'll learn

This revision guide covers the fundamental properties of waves and the key differences between transverse and longitudinal waves. You'll learn how to describe waves using precise scientific terminology, calculate wave speed using the wave equation, and identify real-world examples of both wave types. These concepts form the foundation for understanding sound, light, and the electromagnetic spectrum in your AQA GCSE Physics exam.

Key terms and definitions

Wave — a disturbance that transfers energy from one place to another without transferring matter

Transverse wave — a wave in which the oscillations (vibrations) are perpendicular to the direction of energy transfer

Longitudinal wave — a wave in which the oscillations are parallel to the direction of energy transfer

Amplitude — the maximum displacement of a point on a wave from its rest position, measured in metres (m)

Wavelength — the distance between two adjacent corresponding points on a wave (e.g., crest to crest), measured in metres (m), symbol λ (lambda)

Frequency — the number of complete waves passing a point per second, measured in hertz (Hz)

Period — the time taken for one complete wave to pass a point, measured in seconds (s)

Wave speed — the distance travelled by a wave per second, measured in metres per second (m/s)

Core concepts

Transverse waves

Transverse waves have oscillations perpendicular to the direction of energy transfer. If you picture a wave travelling horizontally from left to right, the particles of the medium (or the oscillation of the wave itself) move up and down vertically.

Key features of transverse waves:

• Can travel through solids and on the surface of liquids
• Cannot travel through the bulk of liquids or gases (except electromagnetic waves, which need no medium)
• Can be polarised (filtered to vibrate in one plane only)
• Show clear peaks (crests) and troughs

Examples of transverse waves:

• All electromagnetic waves (radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays)
• Ripples and waves on water surfaces
• Waves on strings (e.g., guitar strings)
• S-waves (secondary seismic waves) produced by earthquakes

Longitudinal waves

Longitudinal waves have oscillations parallel to the direction of energy transfer. The particles of the medium vibrate back and forth in the same direction as the wave travels.

Key features of longitudinal waves:

• Can travel through solids, liquids and gases
• Cannot be polarised (no single plane of vibration)
• Show compressions (regions where particles are pushed together) and rarefactions (regions where particles are spread apart)
• Require a medium to travel through

Examples of longitudinal waves:

• Sound waves in air, water and solids
• P-waves (primary seismic waves) produced by earthquakes
• Ultrasound waves
• Pressure waves in gases and liquids

Wave properties and measurements

All waves, whether transverse or longitudinal, share common measurable properties.

Amplitude (A):

The amplitude is measured from the rest position (equilibrium) to the maximum displacement. For a transverse wave, this is the height from the middle line to a crest (or to a trough). For a longitudinal wave, amplitude relates to how compressed the compressions are, or how spread out the rarefactions are. Greater amplitude means more energy is being transferred by the wave.

Wavelength (λ):

For transverse waves, wavelength is most easily measured from one crest to the next crest, or one trough to the next trough. For longitudinal waves, wavelength is the distance from the centre of one compression to the centre of the next compression (or rarefaction to rarefaction). Wavelength is always measured in metres, though you may need to convert from centimetres or millimetres in exam questions.

Frequency (f):

Frequency tells you how many complete waves pass a fixed point each second. A frequency of 50 Hz means 50 complete waves pass per second. Frequency is directly related to the energy of the wave — higher frequency means more energy transfer per second (for waves of the same amplitude).

Period (T):

The period is the time for one complete wave cycle. It is the reciprocal of frequency:

Period = 1 ÷ frequency or T = 1/f

If frequency is 5 Hz, the period is 1/5 = 0.2 s.

The wave equation

The relationship between wave speed, frequency and wavelength is fundamental to all wave calculations at GCSE:

wave speed = frequency × wavelength

v = f λ

Where:

• v = wave speed in metres per second (m/s)
• f = frequency in hertz (Hz)
• λ = wavelength in metres (m)

This equation appears on the AQA Physics equation sheet, but you must be confident in rearranging it:

• λ = v/f
• f = v/λ

Important points for calculations:

• Always ensure wavelength is converted to metres before calculating
• Wave speed for electromagnetic waves in a vacuum is 3 × 10⁸ m/s (300,000,000 m/s or 300,000 km/s)
• Sound travels at approximately 330 m/s in air (the exact value varies with temperature)
• Show all working clearly for method marks

Representing waves graphically

Waves can be represented using displacement-distance graphs or displacement-time graphs.

Displacement-distance graph:

This shows a "snapshot" of the wave at one instant in time. The horizontal axis shows distance along the wave, and the vertical axis shows displacement from rest position. You can read the wavelength directly from this graph (distance from crest to crest). You can read the amplitude as the maximum displacement from the rest position (middle line).

Displacement-time graph:

This shows how one point on the wave moves up and down (or back and forth) over time. The horizontal axis shows time, and the vertical axis shows displacement. You can read the period (time for one complete oscillation) directly from this graph. The amplitude is again the maximum displacement from rest position. To find frequency, calculate 1/period.

Comparing transverse and longitudinal waves

Understanding the differences and similarities is essential for exam success:

Both wave types transfer energy without transferring matter. Both obey the wave equation v = fλ. Both can be reflected, refracted and diffracted.

Worked examples

Example 1: Calculating wave speed

Question: A water wave has a frequency of 2 Hz and a wavelength of 0.5 m. Calculate the wave speed. (3 marks)

Answer:

Step 1: Write down the equation v = f λ (1 mark)

Step 2: Substitute values v = 2 × 0.5 (1 mark)

Step 3: Calculate and give unit v = 1 m/s (1 mark)

Examiner tip: Always include the unit for full marks, even if the question doesn't explicitly ask for it.

Example 2: Calculating wavelength

Question: Radio waves travel at 3 × 10⁸ m/s. A radio station broadcasts at a frequency of 95.8 MHz (95,800,000 Hz). Calculate the wavelength of these radio waves. (3 marks)

Answer:

Step 1: Rearrange equation λ = v/f (1 mark)

Step 2: Substitute values λ = (3 × 10⁸) ÷ (9.58 × 10⁷) (1 mark)

Step 3: Calculate λ = 3.13 m (1 mark)

Examiner tip: When dealing with large numbers in standard form, be careful with your calculator input. Check your answer makes sense — radio wavelengths are typically a few metres.

Example 3: Describing wave types

Question: A student observes waves on a slinky spring. Describe how the student could produce: (a) a transverse wave (2 marks) (b) a longitudinal wave (2 marks)

Answer:

(a) Move one end of the slinky from side to side (or up and down) (1 mark), perpendicular to the length of the spring (1 mark).

(b) Push and pull one end of the slinky (1 mark) along the direction of the spring/parallel to its length (1 mark).

Examiner tip: The key words are "perpendicular" for transverse and "parallel" for longitudinal. You must relate the direction of movement to the direction of energy transfer.

Example 4: Using period and frequency

Question: A sound wave has a period of 0.004 s. (a) Calculate the frequency of the sound wave. (2 marks) (b) The speed of sound in air is 330 m/s. Calculate the wavelength. (3 marks)

Answer:

(a) Step 1: Use equation f = 1/T f = 1 ÷ 0.004 (1 mark) f = 250 Hz (1 mark)

(b) Step 1: Use equation λ = v/f λ = 330 ÷ 250 (1 mark) λ = 1.32 m (1 mark for value, 1 mark for unit)

Common mistakes and how to avoid them

• Confusing amplitude with wavelength — Remember amplitude is measured from the rest position to the peak (or trough), not from peak to trough. Wavelength is the distance between two corresponding points.

• Forgetting to convert units — Always convert centimetres to metres (divide by 100), millimetres to metres (divide by 1000), or kilohertz/megahertz to hertz before using the wave equation. Show your conversion in your working.

• Mixing up transverse and longitudinal descriptions — Sound is always longitudinal (even in solids), and light is always transverse. Don't describe sound waves as having "crests and troughs" — use compressions and rarefactions.

• Not showing working in calculations — Even if you get the final answer wrong, you can gain method marks by showing v = fλ or the appropriate rearrangement. Never just write a final number.

• Claiming waves transfer matter — Waves transfer energy and information, but the particles of the medium only oscillate about their rest position. The medium itself doesn't travel with the wave.

• Incorrectly rearranging the wave equation — Practice the triangle method or algebraic rearrangement. If v = fλ, then λ = v/f and f = v/λ. Check by substituting simple numbers.

Exam technique for "Waves: transverse and longitudinal waves, wave properties"

• Command word awareness — "Describe" requires you to state features or characteristics (e.g., "the oscillations are perpendicular to energy transfer"). "Explain" requires reasons or causes (e.g., "the wave transfers energy because particles oscillate and pass energy to neighbouring particles").

• Diagrams must be clear and labelled — If asked to sketch a wave, use a ruler for straight lines (axes), draw smooth curves for transverse waves, and clearly label wavelength and amplitude with arrows. For longitudinal waves, show compressions as dense coils/lines and rarefactions as spread-out coils/lines.

• Structure calculations methodically — Write the equation, substitute values with units, then calculate. This three-step approach guarantees method marks even if you make an arithmetic error. Always give units in your final answer.

• Precision in definitions — Learn key definitions word-perfectly, especially for transverse and longitudinal waves. Examiners look for "perpendicular to direction of energy transfer" and "parallel to direction of energy transfer" — vague descriptions lose marks.

Quick revision summary

Waves transfer energy without transferring matter. Transverse waves have oscillations perpendicular to energy transfer (light, EM waves, water waves); longitudinal waves have oscillations parallel to energy transfer (sound, ultrasound). Key properties are amplitude (maximum displacement), wavelength (distance between corresponding points), frequency (waves per second), and period (time for one wave). Use v = fλ for all wave speed calculations. Know examples of both wave types and understand graphical representations.