Home · IGCSE Physics 0625 · Unit 3 revision
Revision notes · Unit 3 of 6

Waves

How energy travels without matter: ripples, rays, the electromagnetic family, and sound.

Syllabus 3.1 to 3.4 Tier Core + Extended Prepared by the TheLucidSTEM team

§ 3.1 General properties of waves

Key ideas
  • A wave transfers energy without transferring matter: the water bobs on the spot while the wave moves on.
  • Wavelength λ: distance between two adjacent crests (or any two points in step). Amplitude: maximum displacement from the rest position. Frequency f: number of waves passing a point each second, in hertz. A wavefront joins points moving in step.
  • Transverse waves vibrate at right angles to the direction of travel (light, water ripples); longitudinal waves vibrate parallel to it (sound), forming compressions and rarefactions.
  • Waves can be reflected, refracted and diffracted; a ripple tank demonstrates all three.
  • Extended: diffraction through a gap is strongest when the gap width is similar to the wavelength.
Equations
v = f λwave speed = frequency × wavelengthm/s
transverse λ (wavelength) amplitude longitudinal compression rarefaction
Fig. 1 · Transverse: vibration at right angles to travel, with amplitude measured from the rest position. Longitudinal: vibration along the travel direction, one wavelength being compression to compression.
Watch out: amplitude is measured from the rest position to a crest, not from crest to trough. The crest-to-trough distance is twice the amplitude.

§ 3.2 Light

Key ideas
  • Law of reflection: angle of incidence = angle of reflection, both measured from the normal.
  • A plane mirror image is virtual, upright, the same size, laterally inverted, and as far behind the mirror as the object is in front.
  • Refraction: light changes speed at a boundary; entering a denser medium it slows and bends towards the normal, leaving it speeds up and bends away. Frequency never changes.
  • Total internal reflection: inside the denser medium, light hitting the boundary beyond the critical angle is entirely reflected back; this guides light along optical fibres for telecommunications.
  • A converging lens brings parallel rays to the principal focus; the focal length is the lens-to-focus distance. An object beyond F gives a real, inverted image; an object inside F gives a virtual, upright, magnified image (a magnifying glass).
  • Dispersion: a prism splits white light into the spectrum because violet is refracted more than red.
Equations
n = sin i / sin rrefractive index from the angles at the boundary (Extended)no unit
n = 1 / sin crefractive index from the critical angle (Extended)no unit
magnification = hi / hoimage height ÷ object height (Extended)no unit
incident ray reflected ray normal i r mirror
Fig. 2 · Reflection at a plane mirror: angle i equals angle r, and both are measured between the ray and the normal, never the mirror surface.
normal i r air glass bends towards the normal
Fig. 3 · Refraction into glass: the ray slows down and bends towards the normal, so angle r is smaller than angle i; leaving the glass it does the reverse.
i < c i = c i > c escapes angle = c air glass no escape: TIR
Fig. 4 · From glass towards air: below the critical angle the ray refracts out (bending away from the normal); at c it skims the surface; beyond c it is totally internally reflected.
converging lens F F object image
Fig. 5 · A converging lens: the ray parallel to the axis refracts through F, and the ray through the centre goes straight on; where they cross is the real, inverted image.
Watch out: i, r and c are always measured from the normal, not from the surface. A ray hitting a mirror at "30° to the mirror" has an angle of incidence of 60°.

§ 3.3 Electromagnetic spectrum

Key ideas
  • In order of increasing frequency (decreasing wavelength): radio, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays.
  • All EM waves are transverse and travel at the same speed in a vacuum (and approximately in air).
  • Uses: radio for broadcasting; microwaves for cooking and satellite links; infrared for remote controls and thermal imaging; ultraviolet for security marking and sterilising; X-rays for medical imaging and security scanning; gamma for sterilising equipment and treating cancer.
  • Harmful effects: ultraviolet damages skin and eyes; X-rays and gamma rays are ionising and can damage living cells.
  • Extended: a digital signal can be regenerated exactly, so it picks up less noise than analogue and carries more information.
Equations
c = 3.0 × 10⁸ m/sthe speed of every electromagnetic wave in a vacuumm/s
wavelength increases radio microwave infrared visible ultraviolet X-rays gamma frequency and energy increase
Fig. 6 · The electromagnetic spectrum in order: radio waves have the longest wavelength, gamma rays the shortest, and every member travels at 3.0 × 10⁸ m/s in a vacuum.
Watch out: gamma rays are not "faster" than radio waves. In a vacuum every EM wave moves at the same speed; what changes along the spectrum is frequency and wavelength.

§ 3.4 Sound

Key ideas
  • Sound is a longitudinal wave made by a vibrating source; it needs a medium, so it cannot cross a vacuum.
  • The human audible range is 20 Hz to 20 000 Hz; ultrasound is above 20 kHz (medical scanning, sonar).
  • Sound travels at roughly 340 m/s in air, faster in liquids, and fastest in solids.
  • Larger amplitude means a louder sound; higher frequency means a higher pitch.
  • An echo is reflected sound; the sound covers the distance to the surface and back again.
Equations
v = 2d / tspeed from an echo: there-and-back distance ÷ timem/s
Watch out: in echo problems the sound travels there and back. A 0.5 s echo from a wall 85 m away gives v = (2 × 85) ÷ 0.5 = 340 m/s; forgetting the 2 halves the answer.