Waves

Progressive and stationary waves, refraction, superposition, interference, and diffraction.

Spec Points Covered
  • I can describe the difference between transverse and longitudinal progressive waves.
  • I can define amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m)., frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz)., periodThe time taken for one complete oscillation or wave cycle. Measured in seconds (s)., wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m)., and wave speedThe distance travelled by a wavefront per unit time., and use $v = f\lambda$.
  • I can describe the electromagnetic spectrum and explain polarisationThe restriction of oscillations of a transverse wave to a single plane. Only transverse waves can be polarised. of transverse waves.
  • I can apply Snell's law and calculate the critical angleThe angle of incidence at which the refracted ray travels along the boundary (angle of refractionThe change in direction of a wave as it passes from one medium to another, caused by a change in wave speed. = 90 degrees). For angles greater than this, total internal reflection occurs. for total internal reflectionThe complete reflection of a wave at a boundary when the angle of incidence exceeds the critical angleThe angle of incidence at which the refracted ray travels along the boundary (angle of refractionThe change in direction of a wave as it passes from one medium to another, caused by a change in wave speed. = 90 degrees). For angles greater than this, total internal reflection occurs. and the wave travels from a denser to a less dense medium..
  • I can explain the conditions for constructive and destructive interference using path differenceThe difference in distance travelled by two waves from their sources to a given point. Determines whether constructive or destructive interference occurs. and coherenceTwo wave sources are coherent if they have the same frequency and a constant phase relationship..
  • I can use the double-slit equation $\lambda = ax/D$ to determine wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m). from fringe spacing.
  • I can use d sin $\theta = n\lambda$ for diffraction gratingAn optical component with many equally spaced parallel slits that produces sharp interference maxima at specific angles. calculations, including finding maximum order.
  • I can describe stationary waves, identify nodes and antinodes, and draw harmonic patterns on strings and in pipes.
  • I can explain the relationship between intensityThe powerThe rate of energy transfer. Measured in watts (W). transmitted per unit area perpendicular to the wave direction. Measured in W m⁻². Proportional to amplitude squared. and amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m). (I ∝ A²).
Notes
01 Progressive wave Progressive wave → 02 Wave speed Wave speed → 03 Polarisation Polarisation → 04 Refraction Refraction → 05 Principle of superposition Principle of superposition → 06 A single slit first diffracts light to ensure both double slits receive coherent wavefronts $\lambda = \frac{ax}{D}$ → 07 Diffraction grating Diffraction grating → 08 Stationary wave Stationary wave →
Σ Key Equations Full Reference →
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Wave equation
$$v = f\lambda$$
  • Where:
    • $v$ = m \(s^{-1}\)
    • $f$ = Hz
    • $\lambda$ = m
Applies to all waves. Speed depends on medium, not source.
Period–frequency relationship
$$T = \frac{1}{f}$$
  • Where:
    • $T$ = s
    • $f$ = Hz
Period is the reciprocal of frequency.
Snell's law of refraction
$$n_{1} \sin\theta_{1} = n_{2} \sin\theta_{2}$$
  • Where:
    • $n$ = dimensionless
    • $\theta$ = degrees or radians
n = c/v for each medium. Angles measured from the normal.
Critical angle
$$\sin\theta_{c} = \frac{n_{2}}{n_{1}}$$
  • Where:
    • $\theta_c$ = degrees or radians
Derived from Snell's law with θ₂ = 90°. For glass–air: sin θ_c = 1/n_glass. Must be memorised.
Young's double-slit equation
$$\lambda = \frac{ax}{D}$$
  • Where:
    • $\lambda$ = m
    • $a$ = m
    • $x$ = m
    • $D$ = m
Requires D >> a. x is the fringe spacing between adjacent bright fringes.
Diffraction grating equation
$$d\sin\theta = n\lambda$$
  • Where:
    • $d$ = m
    • $\theta$ = degrees or radians
    • $\lambda$ = m
d = 1/(lines per metre). n is the order number (integer). Maximum order when sin θ = 1.
Intensity–amplitude relationship
$$I \propto A^{2}$$
  • Where:
    • $I$ = W \(m^{-2}\)
    • $A$ = m
Doubling amplitude quadruples intensity. Applies to all progressive waves.
Refractive index
$$n = \frac{c}{v}$$
  • Where:
    • $n$ = dimensionless
    • $c$ = m \(s^{-1}\)
    • $v$ = m \(s^{-1}\)
c = speed of light in vacuum, v = speed of light in the medium. n is always ≥ 1.