Wave Properties and Superposition

Wave properties

Waves transfer energy without transferring matter.

• Transverse: oscillations perpendicular to energy transfer (all EM waves, water waves). Can be polarised.
• Longitudinal: oscillations parallel to energy transfer, as compressions and rarefactions (sound).

Key quantities: amplitude, wavelength (λ), frequency (f), period (T = 1/f), and:

wave speed  v = fλ

Phase and path difference

• Phase difference — how far through their cycles two points are, measured in radians or degrees (a full cycle = 2π rad = 360°).
• Points in phase are a whole number of wavelengths apart; antiphase (out of phase) points are an odd number of half-wavelengths apart.

Polarisation

Only transverse waves can be polarised — restricted to oscillate in one plane. Evidence that light is transverse. Used in polarising sunglasses and to reduce glare.

Superposition

When two waves meet, their displacements add (the principle of superposition):

• Constructive interference: waves in phase → larger amplitude.
• Destructive interference: waves in antiphase → cancel out.

For a stable interference pattern, sources must be coherent (same frequency and a constant phase difference) and similar amplitude.

Two-source interference & diffraction gratings

• Young's double-slit: light through two slits produces bright and dark fringes. Fringe spacing: w = λD ÷ s (D = distance to screen, s = slit separation).
• Diffraction grating: many slits give sharper, brighter maxima: d sin θ = nλ (d = grating spacing, n = order).

Stationary (standing) waves

Formed when two identical waves travelling in opposite directions superpose (e.g. a wave reflected back on itself).

• Nodes — points of zero amplitude (destructive); antinodes — points of maximum amplitude.
• No net energy is transferred along a stationary wave.
• On a string, the fundamental frequency has a wavelength of 2L (nodes at each end).

Worked example

Two coherent sources produce waves that arrive at a point with a path difference of exactly 2λ. What interference occurs?

• A path difference of a whole number of wavelengths (2λ) means the waves arrive in phase → constructive interference (maximum amplitude). ✓

Common mistakes

• Saying longitudinal waves can be polarised — only transverse waves can.
• Forgetting that a stable interference pattern needs coherent sources.
• Mixing up nodes (zero) and antinodes (maximum) on stationary waves.

Exam tips

• Learn v = fλ and the interference conditions (whole λ = constructive, half λ = destructive).
• State coherence and path/phase difference in interference explanations.
• Distinguish progressive waves (transfer energy) from stationary waves (nodes/antinodes, no net transfer).

Key facts to remember

• v = fλ; transverse (can be polarised) vs longitudinal (sound).
• Superposition: in phase → constructive, antiphase → destructive; stable patterns need coherent sources; grating d sin θ = nλ.
• Stationary waves = two opposite waves superposing → nodes (zero) and antinodes (max); no net energy transfer.