Progressive Waves

Wave properties, the wave equation, phase difference, and displacement-time graphs.

Spec Points Covered
  • Define a progressive waveA wave that transfers energyThe capacity to do work. Measured in joules (J). from one place to another without transferring matter. and distinguish it from 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..
  • Define and use the terms displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m)., amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m)., wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m)., periodThe time taken for one complete oscillation or wave cycle. Measured in seconds (s)., frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). and wave speedThe distance travelled by a wavefront per unit time..
  • Apply the wave equation $v = f \lambda$ to calculate wave speedThe distance travelled by a wavefront per unit time., frequencyThe number of complete oscillations passing a point per unit time. Measured in hertz (Hz). or wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m)..
  • Describe and calculate phase differenceThe fraction of a cycle by which one wave leads or lags behind another, measured in degrees or radians. in degrees, radians or fractions of a wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m)..
  • Interpret displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m).-time and displacementThe distance moved in a particular direction from a starting point. A vector quantity. Measured in metres (m).-distance graphs for transverse waves.
  • State and apply the relationship between frequency and periodThe time taken for one complete oscillation or wave cycle. Measured in seconds (s).: $f = 1/T$.
Notes
01 A progressive wave transfers energy without transferring the medium Progressive wave 3.3.1.1 → 02 Five quantities define any progressive wave Displacement (x) 3.3.1.1 → 03 Frequency and period are reciprocals of each other $f = \frac{1}{T}$ 3.3.1.1 → 04 The wave equation links speed, frequency and wavelength $v = f\lambda$ 3.3.1.1 → 05 Worked example: wave equation with period 3.3.1.1 → 06 Phase difference measures how far one wave is ahead of another Phase difference 3.3.1.1 → 07 Worked example: reading amplitude, wavelength and phase from a diagram 3.3.1.1 → 08 Intensity is proportional to the square of amplitude $I \propto A^{2}$ 3.3.1.1 →
Σ Key Equations Full Reference →
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Wave equation
$$v = f\lambda$$
  • Where:
    • $v$ = wave speed (m \(s^{-1}\))
    • $f$ = frequency (Hz)
    • $\lambda$ = wavelength (m)
Applies to all waves. For EM waves in a vacuum, v = c = \(3 \times 10^{8}\) m/s.
Intensity-amplitude relationship
$$I \propto A^{2}$$
  • Where:
    • $I$ = intensity (W \(m^{-2}\))
    • $A$ = amplitude (m)
Doubling amplitude quadruples intensity. Used in interference and diffraction analysis.
Frequency-period relationship
$$f = \frac{1}{T}$$
  • Where:
    • $f$ = frequency (Hz)
    • $T$ = period (s)
Read T from a displacement-time graph as the time for one complete cycle.
Q Retrieval Practice All 10 Questions →
Q1. Define a progressive waveA wave that transfers energyThe capacity to do work. Measured in joules (J). from one place to another without transferring matter..
A wave that transfers energy from one point to another without transferring the medium itself.
Q2. Define the amplitudeThe maximum displacement of a point on a wave from its equilibrium (rest) position. Measured in metres (m). of a wave.
  • The maximum displacement of a particle in the wave from its equilibriumAn object is in equilibrium when the resultant force on it is zero. The object is either stationary or moving at constant velocityThe rate of change of displacement. A vector quantity. Measured in m s⁻¹.. position.
  • Measured in metres.
Q3. Define the wavelength of a wave.
  • The distance between points on successive oscillations that are in phase.
  • Measured in metres.
Q4. State the relationship between frequency and periodThe time taken for one complete oscillation or wave cycle. Measured in seconds (s)..
  • f = 1/T.
  • Frequency is the reciprocal of period.
Q5. State the wave equation.
v = f lambda, where v is wave speedThe distance travelled by a wavefront per unit time. (m/s), f is frequency (Hz), and lambda is wavelength (m).