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Theme C — Wave Behaviour

Theme C — Wave Behaviour — IB Physics SL Revision Notes & Topical Questions

5 min read 9 parts Lesson 1 of 31 Unit quiz

📚 IB Physics SL 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

Theme C — Wave Behaviour — IB PHYSICS SL notes: Summarise simple harmonic motion, wave properties, sound, refraction, diffraction, interference, standing waves and the Doppler effect at SL level.Simple harmonic motion (SHM) — oscillation in which the acceleration is proportional …

  • Mass on a spring
  • Simple pendulum
  • Energy transfer
  • Transverse wave
  • Longitudinal wave
  • Wavelength

Part 1 of 7Simple harmonic motion

1Simple harmonic motion (SHM)
  • Simple harmonic motion (SHM) oscillation in which the acceleration is proportional to the displacement from equilibrium and directed towards it
  • The period does not depend on the amplitude.
2Mass on a spring
  • T = 2π√(m/k)
    What the symbols mean: T = period (s) · m = mass on the spring (kg) · k = spring constant (N m−1)
3Simple pendulum
  • T = 2π√(L/g) for small angles
4Energy
  • Energy it is exchanged between kinetic and potential forms
  • For an ideal system the total energy ½kx02 stays constant.
  • With damping the amplitude decays.

Part 2 of 7Wave model

Energy transfer
  • Energy transfer waves transfer energy without transferring matter
Transverse wave
  • Transverse wave the oscillation is perpendicular to the direction of travel
Longitudinal wave
  • Longitudinal wave the oscillation is parallel to the direction of travel
  • It produces compressions (pressure above normal) and rarefactions (pressure below normal).
Wavelength
  • Wavelength the distance between neighbouring points that are in phase
Medium
  • Medium mechanical waves need a medium, electromagnetic waves do not
Wave equation
  • Wave equation v = fλ
    What the symbols mean: v = wave speed (m s−1) · f = frequency (Hz) · λ = wavelength (m)

Part 3 of 7Sound

Sound
Nature
  • Nature sound is a longitudinal wave
Speed in different media
  • Speed in different media solids are fastest, then liquids, then gases
  • It is about 340 m s−1 in air at 20 °C, 1500 m s−1 in water and 5000 m s−1 in steel.
  • Particles in solids are bound more strongly and respond more quickly.
Gases
  • Gases the speed rises with temperature and does not depend on pressure at fixed temperature
Frequency
  • Frequency it does not affect the speed, so low and high notes arrive together
  • Raising the pitch shortens the wavelength.
Hearing range
  • Hearing range about 20 Hz to 20 kHz
Loudness
  • Loudness it relates to amplitude and intensity, I ∝ amplitude2, in W m−2
  • Sound levels use the logarithmic decibel scale.
Quality (timbre)
  • Quality (timbre) it depends on the mixture of frequencies present
  • A violin and a flute playing the same note share a fundamental but have different overtones.
Echoes
  • Echoes a distinct echo needs a delay of more than about 0.1 s
  • The distance to a reflector is d = vt/2.
  • This is the principle of sonar and ultrasound imaging.
Diffraction
  • Diffraction low-frequency sound diffracts around corners more than high-frequency sound

Part 4 of 7Refraction, diffraction and interference

1Refraction
  • Refraction it changes speed and wavelength but not frequency
2Refractive index
  • Refractive index n = c/v and Snell's law is n1 sin θ1 = n2 sin θ2
3Total internal reflection
  • Total internal reflection the wave must travel from a denser to a less dense medium at an angle above the critical angle
4Diffraction
  • Diffraction it is greatest when the gap is about one wavelength
  • A narrower slit or longer wavelength gives more spreading.
  • Wavelength, frequency and speed are unchanged.
5Interference
  • Interference it is constructive when the path difference is nλ and destructive when it is (n + ½)λ
6Double slit
  • Double slit the fringe separation is s = λD/d
  • Fringes are wider for a longer wavelength, larger D or smaller d.

Part 5 of 7Standing waves and harmonics

1Features
  • Features a standing wave has nodes of zero amplitude and antinodes of maximum amplitude
  • Adjacent nodes are λ/2 apart.
2String or open pipe
  • String or open pipe fn = nv/2L
3Pipe closed at one end
  • Pipe closed at one end only odd harmonics occur, fn = nv/4L
4First overtone
  • First overtone it is the second harmonic in a string or open pipe but the third harmonic in a closed pipe
5Real instruments
  • Real instruments they produce mixtures of harmonics

Part 6 of 7Resonance and instruments

Resonance tube
  • Resonance tube lower a tube into water while a tuning fork of known frequency sounds above it
  • Resonance occurs at air-column lengths of λ/4, 3λ/4 and so on.
  • The difference between successive resonance lengths is λ/2, which cancels the end correction.
Pitch of strings
  • Pitch of strings shortening a guitar string raises the pitch
  • Frequency ratios depend only on the ratio of lengths when the wave speed is unchanged.
Flute
  • Flute it changes its effective length by opening holes
Plucking
  • Plucking plucking at the centre excites odd harmonics strongly for a mellow tone, and plucking near the bridge gives a brighter tone

Part 7 of 7Doppler effect

Moving source
  • Moving source wavefronts ahead of the source are bunched and wavefronts behind are spread out
    • (shorter wavelength, higher frequency)
  • The wave speed in the medium is unchanged.
Moving observer
  • Moving observer with a stationary source the observer crosses wavefronts more often, so the observed frequency rises
Formulae
  • Formulae the two cases differ slightly for sound because a medium defines a frame of rest
  • For light and for speeds much less than the wave speed the results coincide.

Key terms

TermMeaning
Simple harmonic motionOscillation with acceleration proportional to displacement and directed towards equilibrium.
RarefactionA region of a longitudinal wave where the pressure is below normal.
DiffractionThe spreading of a wave at a gap or around an obstacle.
AntinodeA point of maximum amplitude in a standing wave.
FundamentalThe lowest-frequency standing wave of a system.
Doppler effectA change in observed frequency due to relative motion.
TimbreThe quality of a sound that depends on the mixture of frequencies.

Avoid these mistakes

1
Saying wavelength is the length of the wave — it is the distance between neighbouring points in phase.
2
Saying sound travels in a vacuum or that a wave carries the particles along.
3
Using the open-pipe harmonic series for a pipe closed at one end.
4
Believing that higher-frequency sound travels faster in a given medium.
5
Confusing overtones with harmonics.

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