Wave Types, Polarisation & Stationary Waves

Longitudinal vs transverse waves, polarisation, superposition, stationary waves and harmonics.

Spec Points Covered
  • Define transverse and longitudinal waves and give examples of each.
  • Explain why only transverse waves can be polarised.
  • Describe applications of polarisationThe restriction of oscillations of a transverse wave to a single plane. Only transverse waves can be polarised. including polaroid sunglasses and TV aerials.
  • State the principle of superpositionWhen two or more waves meet, the resultant displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m). at any point is the vector sum of the individual displacements. of waves.
  • Explain how stationary waves are formed from two progressive waves.
  • Identify nodes and antinodes and state the phase relationships between points on a stationary waveA wave pattern formed by the superposition of two progressive waves of the same frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). and amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m). travelling in opposite directions. EnergyThe capacity to do work. Measured in joules (J). is not transferred along a stationary wave..
  • Calculate harmonic frequencies from the fundamental frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). and string length.
  • Apply the equation $f = (1/2L) \sqrt{T/\mu}$ for the first harmonic on a string.
  • Describe the required practical for investigating stationary waves on a string.
Notes
01 Transverse waves oscillate perpendicular to the direction of travel Transverse wave 3.3.1.2 → 02 Longitudinal waves oscillate parallel to the direction of travel Longitudinal wave 3.3.1.2 → 03 Polarisation restricts oscillations to a single plane Polarisation 3.3.1.2 → 04 Two crossed polarisers block all light 3.3.1.2 → 05 Polarisation has everyday applications 3.3.1.2 → 06 The principle of superposition: displacements add where waves overlap Principle of superposition 3.3.1.3 → 07 Stationary waves are formed by two identical waves travelling in opposite directions Stationary wave 3.3.1.3 → 08 Nodes have zero displacement; antinodes have maximum displacement Node 3.3.1.3 → 09 Harmonics are the resonant frequencies of a stationary wave on a string 3.3.1.3 → 10 The first harmonic frequency depends on tension and mass per unit length $v = \sqrt{\frac{T}{\mu}}$ 3.3.1.3 → 11 Required practical: investigating stationary waves on a string 3.3.1.3 →
Σ Key Equations Full Reference →
On Data Sheet
Not on Data Sheet
First harmonic frequency
$$f = \frac{1}{2L}\sqrt{\frac{T}{\mu}}$$
  • Where:
    • $f$ = fundamental frequency (Hz)
    • $L$ = vibrating string length (m)
    • $T$ = tension (N)
    • $\mu$ = mass per unit length (kg \(m^{-1}\))
Derived from v = f lambda with lambda = 2L and v = sqrt(T/mu). L is the distance between fixed points.
Wave speed on a string
$$v = \sqrt{\frac{T}{\mu}}$$
  • Where:
    • $v$ = wave speed (m \(s^{-1}\))
    • $T$ = tension (N)
    • $\mu$ = mass per unit length (kg \(m^{-1}\))
Used to verify wave speed from the stationary waves practical.
Harmonic frequencies
$$\begin{aligned} f_n &= nf_1 \\ &= \frac{nv}{2L} \end{aligned}$$
  • Where:
    • $f_n$ = frequency of the nth harmonic (Hz)
    • $n$ = harmonic number (1, 2, 3...)
    • $f_1$ = fundamental frequency (Hz)
    • $v$ = wave speed (m \(s^{-1}\))
    • $L$ = string length (m)
Each harmonic is an integer multiple of the fundamental. The nth harmonic has n antinodes and (n+1) nodes.
Q Retrieval Practice All 12 Questions →
Q1. Define a transverse wave and give two examples.
  • A wave where particles oscillate perpendicular to the direction of wave travel.
  • Examples: visible light (EM wave), waves on a string.
Q2. Define a longitudinal wave and give two examples.
  • A wave where particles oscillate parallel to the direction of wave travel.
  • Examples: sound waves, seismic P-waves.
Q3. Why can longitudinal waves not be polarised?
  • They oscillate parallel to the direction of travel, so there is only one plane of oscillation.
  • PolarisationThe restriction of oscillations of a transverse wave to a single plane. Only transverse waves can be polarised. requires restricting oscillations to one of many possible planes.
Q4. State what polarisationThe restriction of oscillations of a transverse wave to a single plane. Only transverse waves can be polarised. is.
When particle oscillations occur in only one direction perpendicular to the direction of wave propagation.
Q5. Explain how polaroid sunglasses reduce glare from water.
  • Light reflected from water is partially horizontally polarised.
  • Polaroid lenses have vertical transmission axes, so they block the horizontally polarised glare.