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Oscillation in which acceleration is proportional to displacement from equilibrium and directed towards it.
Amplitude (x₀)
Maximum displacement from equilibrium.
Period (T)
Time for one complete oscillation.
Angular frequency (ω)
ω = 2π/T = 2πf, in rad s⁻¹.
Phase angle
Where in its cycle an oscillation is, in radians.
The minus sign in \(a=-\omega^{2}x\) shows the restoring force always points back to equilibrium.
The full notes, worked example, interactive diagram and check questions for this subtopic are in the app.
Exam tip: To show motion is SHM, prove the acceleration (or force) is proportional to displacement and opposite in direction.
C.2Wave model
Key terms
Transverse wave
Oscillations are perpendicular to the direction of energy transfer (e.g. light, waves on a string).
Longitudinal wave
Oscillations are parallel to the direction of energy transfer, with compressions and rarefactions (e.g. sound).
Wavelength (λ)
Distance between two adjacent points in phase, in m.
Frequency (f)
Number of oscillations per second, in Hz.
Electromagnetic wave
A transverse wave of oscillating electric and magnetic fields that travels at c = 3.00 × 10⁸ m s⁻¹ in a vacuum.
Waves transfer energy without transferring matter: particles of the medium oscillate about fixed positions.
The full notes, worked example, interactive diagram and check questions for this subtopic are in the app.
Exam tip: Check which graph you are given: a distance axis gives wavelength, a time axis gives period.
C.3Wave phenomena
Key terms
Refraction
Change in direction of a wave when its speed changes as it crosses a boundary.
Refractive index (n)
n = c/v: how much a medium slows light.
Critical angle
Angle of incidence for which the refracted angle is 90°; above it there is total internal reflection.
Diffraction
Spreading of a wave through a gap or around an obstacle; strongest when the gap is about λ.
Coherent sources
Sources with the same frequency and a constant phase difference.
Path difference
Difference in the distances travelled by two waves to a point.
Light bends towards the normal when it enters a denser (higher \(n\)) medium; frequency stays the same while speed and wavelength fall.
The full notes, worked example, interactive diagram and check questions for this subtopic are in the app.
Exam tip: Measure across several fringes and divide, which reduces the percentage uncertainty in s.
C.4Standing waves and resonance
Key terms
Standing wave
Pattern formed by the superposition of two identical waves travelling in opposite directions; energy is not transferred.
Node
Point of zero amplitude on a standing wave.
Antinode
Point of maximum amplitude on a standing wave.
Harmonic
A possible standing-wave mode; the first harmonic (fundamental) has the lowest frequency.
Resonance
Large-amplitude oscillation when the driving frequency equals the natural frequency.
Damping
Loss of energy from an oscillating system, reducing amplitude.
Nodes are half a wavelength apart. A string fixed at both ends has nodes at the ends; an open end of a pipe is an antinode, a closed end is a node.
The full notes, worked example, interactive diagram and check questions for this subtopic are in the app.
Exam tip: Sketch the standing-wave pattern first, then read the wavelength off the drawing.
C.5Doppler effect
Key terms
Doppler effect
The change in observed frequency when the source and observer move relative to each other.
Redshift
Increase in observed wavelength of light from a receding source.
Blueshift
Decrease in observed wavelength of light from an approaching source.
An approaching source squashes the wavefronts together (higher frequency); a receding source spreads them out (lower frequency). The source's own frequency does not change.
The full notes, worked example, interactive diagram and check questions for this subtopic are in the app.
Exam tip: Sanity check: approaching must give a higher frequency, so choose the sign that makes the fraction greater than 1.