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Theme C — Wave Behaviour

C.2.1 Properties of Waves — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 12 of 37 1 quiz

📚 IB Physics HL Hub / Topical Revision
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Curriculum Equation Key Wave Speed & Doppler Effect FormulasFast Exam Solution
v = f × λ | f_obs = f × (v ± v_o) / (v ∓ v_s) | T = 1 / f
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Lesson summary

C.2.1 Properties of Waves — IB PHYSICS SL notes: Describe a wave using displacement, amplitude, wavelength, frequency, period and speed, and use v = fλ.Travelling wave — a repeating disturbance that transfers energy from one place to another without transferring matterWaves are g…

  • Particle motion
  • Mechanical waves
  • Electromagnetic waves
  • Displacement x (m)
  • Amplitude x0 (m)
  • Wavelength λ (m)

Part 1 of 7What a wave is

What a wave is
Travelling wave
  • Travelling wave a repeating disturbance that transfers energy from one place to another without transferring matter
  • Waves are generated by oscillating sources and travel away from them.
Particle motion
  • Particle motion each particle of the medium, or point of the field, oscillates about a fixed equilibrium position
  • A cork on a pond bobs up and down as ripples pass but does not travel with them.
Mechanical waves
  • Mechanical waves sound, water waves and waves on a string need a medium whose particles interact
Electromagnetic waves
  • Electromagnetic waves they need no medium and travel through a vacuum

Part 2 of 7Quantities describing a wave

Displacement x (m)
  • Displacement x (m) the distance of a point from its equilibrium position, which can be positive or negative
Amplitude x0 (m)
  • Amplitude x0 (m) the maximum magnitude of displacement from equilibrium
  • It relates to the energy carried.
Wavelength λ (m)
  • Wavelength λ (m) the shortest distance between two points that are in phase, such as crest to crest
Period T (s)
  • Period T (s) the time for one complete oscillation to pass a fixed point
Frequency f (Hz)
  • Frequency f (Hz) the number of complete oscillations passing a fixed point per second
Wave speed v (m s−1)
  • Wave speed v (m s−1) the distance travelled by the pattern, and hence the energy, per unit time

Part 3 of 7Wave equation

Period and frequency
  • Period and frequency f = 1/T
    What the symbols mean: T = period, the time for one complete wave (s) · f = frequency (Hz)
  • The source sets the frequency, and it does not change when the wave enters a new medium.
Derivation
  • Derivation in one period the pattern advances one wavelength, so v = λ/T, which gives v = fλ
For light
  • For light in a vacuum v is replaced by c, so c = fλ
Constant speed
  • Constant speed a higher frequency means a shorter wavelength, and a longer wavelength means a lower frequency

Part 4 of 7Reading wave graphs

1Displacement–distance graph
  • Displacement–distance graph a snapshot at one instant that shows the wave shape along the direction of travel
  • The spacing between neighbouring peaks is the wavelength.
  • The maximum height is the amplitude.
2Displacement–time graph
  • Displacement–time graph it follows one point as time passes
  • The spacing between neighbouring peaks is the period.
  • The maximum height is still the amplitude.
3Marking arrows
  • Marking arrows draw them from the top of one peak to the top of the next, and measure amplitude from equilibrium
4Units
  • Units convert cm to m and ms to s before substituting

Part 5 of 7Phase

1In phase
  • In phase points a whole number of wavelengths apart move together
2Antiphase
  • Antiphase points an odd number of half-wavelengths apart always move in opposite directions
3Phase difference
  • Phase difference for two points a distance d apart it is 2πd/λ radians, or 360°d/λ

Part 6 of 7Wavefronts and intensity

Wavefront
  • Wavefront a line or surface joining points of the same phase
  • The ray is the direction of travel and is perpendicular to the wavefront.
Intensity
  • Intensity the energy per second passing through unit area at right angles to the wave, in W m−2
Amplitude link
  • Amplitude link intensity is proportional to the square of the amplitude, I ∝ x02
  • Doubling the amplitude quadruples the intensity.
Point source
  • Point source the energy spreads over a sphere, so I ∝ 1/r2
Sinusoidal form
  • Sinusoidal form a travelling sinusoidal wave shows as a sine curve in both kinds of graph

Part 7 of 7More from the specification

1Transverse vs Longitudinal Waves
  • Waves are classified by particle vibration direction: in transverse waves vibrations are perpendicular to the direction waves propagate,
  • while in longitudinal waves oscillations are parallel.
2Wave Equation
  • The wave equation relates wave speed v (in m/s), frequency f (in Hz),
  • and wavelength lambda as v = f * lambda, applicable across all mechanical and electromagnetic waves.
    • (defined in metres)
3Electromagnetic Spectrum
  • Electromagnetic waves propagate through vacuum at 3.0 * 108 m/s, spanning a continuous spectrum of wavelengths from gamma rays to radio waves.
4Audible Sound Wave Range
  • Sounds propagate as mechanical longitudinal compression waves through matter, with normal human hearing spanning an audible frequency range of 20 Hz to 20 kHz.
5Spectrum
  • Range of colours in white light.
6Longitudinal wave
  • Wave whose vibrations are parallel to the direction of travel
7Transverse wave
  • Wave whose vibration is at right angles to the direction of propagation
8Electromagnetic spectrum
  • Continuous family of waves from radio waves to gamma rays

Key terms

TermMeaning
AmplitudeMaximum magnitude of displacement from equilibrium.
WavelengthShortest distance between two points in phase.
PeriodTime for one complete oscillation, T = 1/f.
FrequencyNumber of oscillations per second, in hertz.
WavefrontA line or surface of points that are in phase.
IntensityPower per unit area received perpendicular to the wave direction.
Phase differenceFraction of a cycle by which two points are out of step.

Avoid these mistakes

1
Reading wavelength from a displacement–time graph — the horizontal spacing there is the period.
2
Thinking the particles of the medium travel along with the wave — they only oscillate about equilibrium.
3
Quoting amplitude as peak-to-peak height — it is measured from equilibrium to a peak.
4
Saying frequency changes when a wave enters a new medium — the source fixes the frequency.
5
Forgetting that intensity depends on amplitude squared, not amplitude.

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