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Physics 06253.1

General properties of waves

Transverse and longitudinal waves, wavelength, frequency, amplitude, the wave equation, reflection, refraction and diffraction.

Learning objectives

What you need to be able to do

Teacher-mapped phrasing — check against the official Cambridge syllabus for exact wording.

  • 3.1.1Describe what is meant by wavefronts, wavelength, frequency, crest, trough, amplitude and wave speed.
  • 3.1.2Distinguish between transverse and longitudinal waves and give examples of each.
  • 3.1.3Recall and use v = fλ.
  • 3.1.4Describe reflection, refraction and diffraction of waves using a ripple tank.

7 minute read

Wave basics and the wave equation

A wave transfers energy without transferring matter. The particles (or fields) oscillate about a fixed position; they do not travel with the wave.

Two kinds

  • Transverse: oscillations are at right angles to the direction of energy transfer. Examples: all electromagnetic waves, water waves, waves on a rope.
  • Longitudinal: oscillations are parallel to the direction of energy transfer, producing compressions and rarefactions. The example you must know is sound.

The quantities

  • Wavelength (λ): distance between two neighbouring points in phase — crest to crest, in metres.
  • Frequency (f): number of complete waves passing a point per second, in hertz.
  • Amplitude: maximum displacement from the undisturbed position. It is not the distance from crest to trough — that is twice the amplitude.
  • Time period (T): time for one complete wave, and T = 1 / f.

The wave equation

v = fλ — wave speed equals frequency × wavelength.

Because the speed of a wave depends on the medium, when a wave enters a new material its speed and wavelength change but its frequency does not. That single fact explains refraction.

Three behaviours

  • Reflection: the wave bounces off a barrier; the angle of incidence equals the angle of reflection.
  • Refraction: the wave changes speed on entering a new medium, so it changes direction (unless it enters along the normal).
  • Diffraction: the wave spreads out through a gap or around an edge. The spreading is greatest when the gap is about the same size as the wavelength.

Think of it like this

A wave is a stadium Mexican wave: the wave travels around the ground, but every person stays in their own seat. Energy moves; matter does not.

Worked examples

Method, step by step

A sound wave has a frequency of 340 Hz and a wavelength of 1.0 m. Calculate its speed.

  1. 1v = fλ
  2. 2v = 340 × 1.0

v = 340 m/s

A radio station broadcasts at 90 MHz. Radio waves travel at 3.0 × 10⁸ m/s. Calculate the wavelength.

  1. 1Convert: 90 MHz = 9.0 × 10⁷ Hz
  2. 2λ = v / f = 3.0 × 10⁸ / 9.0 × 10⁷

λ = 3.3 m

Common misconceptions

  • Thinking the particles travel along with the wave. They oscillate about a fixed point.
  • Measuring amplitude from crest to trough instead of from the middle to a crest.
  • Saying the frequency changes during refraction. Frequency is set by the source and stays the same.

In the exam

  • For diffraction questions, say explicitly that the effect is greatest when the gap width is comparable to the wavelength.
  • Label ray diagrams with the normal (a dashed line at 90° to the surface) — angles are always measured from the normal, never from the surface.
  • v = fλ questions almost always need a unit conversion first (kHz → Hz, cm → m).