Recall and use the equation for wave speed v = f λ

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3.1 General properties of waves

Wave types (core)

  • Transverse waves – particles of the medium move perpendicular to the direction of travel (e.g. water ripples, light/EM waves).
  • Longitudinal waves – particles of the medium move parallel to the direction of travel (e.g. sound in air, a compression pulse on a slinky, pressure waves in a spring).

Key quantities and symbols (core)

Waves transfer energy without a permanent displacement of matter. The quantities used to describe a wave are listed below.

Quantity Symbol Unit Definition
Amplitude A metre (m) Maximum displacement from the equilibrium line; the distance from the equilibrium line to a crest (positive) or a trough (negative).
Wavelength λ metre (m) Distance between two successive points that are in the same phase (e.g. crest ↔ crest or trough ↔ trough).
Frequency f hertz (Hz) Number of complete cycles that pass a fixed point each second.
Period T second (s) Time taken for one complete cycle; T = 1/f.
Wave speed v metre per second (m s⁻¹) Distance a wave travels per unit time.
Crest – – Highest point of a transverse wave; the point of maximum positive displacement.
Trough – – Lowest point of a transverse wave; the point of maximum negative displacement.
Wave‑front – – Imaginary line (in 2‑D) or surface (in 3‑D) joining points that are in the same phase.

Fundamental relationship between speed, frequency and wavelength (core)

The three core quantities are linked by the equation

\(v = f\,\lambda\)

From this you can solve for any one variable:

  • Speed: \(v = f\lambda\)
  • Frequency: \(f = \dfrac{v}{\lambda}\)
  • Wavelength: \(\lambda = \dfrac{v}{f}\)

Note: If a distance–time graph shows a straight‑line segment, the gradient of that segment is the wave speed v. This value can be combined with a measured frequency to find the wavelength using the same equation.

Diagram of a transverse wave showing a crest, trough, wavelength (λ) and direction of travel (v)
Transverse wave – crest, trough, wavelength (λ) and direction of travel (v).

Core wave phenomena (core)

  • Reflection – the wave bounces back from a surface. Law of reflection: angle of incidence = angle of reflection.
    Sketch of a wave reflecting from a plane surface, showing equal angles of incidence and reflection
  • Refraction – change of speed (and therefore direction) when a wave passes into a different medium. For light the quantitative law is Snell’s law (optional for core); the qualitative idea is that the wave bends towards the normal if it slows down.
    Sketch of a wave changing direction at the boundary between two media
  • Diffraction – bending of a wave as it passes through a narrow gap or around an obstacle. The effect is most noticeable when the gap width is comparable to the wavelength.
    Sketch of a wave spreading after passing through a narrow slit
    • Supplementary point: Diffraction becomes more pronounced as the gap size approaches λ.
  • Interference – superposition of two or more waves leading to constructive or destructive patterns. (Optional, beyond the core assessment.)

Worked example (core)

Question: A sound wave travels through air at \(v = 340\ \text{m s}^{-1}\) and has a frequency of \(f = 680\ \text{Hz}\). Calculate its wavelength.

  1. Write down the known values: \(v = 340\ \text{m s}^{-1}\), \(f = 680\ \text{Hz}\).
  2. Use the rearranged form \(\lambda = \dfrac{v}{f}\).
  3. Substitute the numbers: \(\lambda = \dfrac{340}{680}\ \text{m} = 0.50\ \text{m}\).
  4. Answer: \(\lambda = 0.50\ \text{m}\).

Practical activity – determining wavelength with a ripple tank (core)

This experiment lets students verify \(v = f\lambda\) for water waves.

  1. Set up the ripple tank and place a monochromatic (single‑frequency) wave source.
  2. Adjust the frequency on the wave generator and note the setting (this gives f).
  3. Place a screen or a ruler at a known distance from the source and shine a laser pointer onto the water surface. The reflected laser spots form a series of bright lines corresponding to successive wave‑crests.
  4. Measure the distance between two adjacent bright spots; this distance is the wavelength \(\lambda\).
  5. Measure the time taken for a crest to travel a known distance (or use a video analysis tool) to obtain the wave speed v.
  6. Compare the experimentally obtained \(\lambda\) with the value calculated from \(v = f\lambda\). Discuss any discrepancies and possible sources of error (e.g., water depth, reflections from tank walls).

Practice questions (core)

  1. A wave on a string has a wavelength of \(0.25\ \text{m}\) and a frequency of \(12\ \text{Hz}\). What is its speed?
  2. The speed of a water wave is \(2.0\ \text{m s}^{-1}\) and its frequency is \(0.5\ \text{Hz}\). Find its wavelength.
  3. If the wavelength of a radio wave is \(3.0\ \text{m}\) and its speed is \(3.0\times10^{8}\ \text{m s}^{-1}\), calculate its frequency.

Summary (core)

  • The three core wave quantities are linked by \(v = f\lambda\). Knowing any two lets you find the third.
  • Increasing the frequency while the speed stays the same shortens the wavelength; decreasing the frequency lengthens it.
  • Always keep units consistent: metres (m) for distance, seconds (s) for time, hertz (Hz) for frequency.
  • Wave types: transverse (particle motion ⟂ to travel) and longitudinal (particle motion ∥ to travel).
  • Core phenomena – be able to describe and sketch reflection, refraction and diffraction; remember that diffraction is strongest when gap size ≈ wavelength.
  • Interference is optional material, not required for the core IGCSE assessment.

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