A-Level Physics: Waves and Stationary Waves

Waves at A-Level split into two connected stories: progressive waves carrying energy, and stationary waves storing it in fixed patterns. This quiz covers both, with the phase-difference calculations that separate secure answers from guesswork.

The progressive-wave questions apply the core relationships with concrete values: wavelength from speed and frequency, speed from wavelength and period, and the behaviour of waves at boundaries — including the π phase change on reflection from a fixed end and the fact that frequency is fixed by the source and survives a change of medium. Phase difference gets two dedicated calculations, both worked from path difference as a fraction of wavelength: one landing at π/2 and one — verified manually during checking — at 3π, the kind of beyond-2π answer that tests whether the method is genuinely understood rather than pattern-matched.

The stationary-wave questions cover formation and properties: why points between adjacent nodes oscillate in phase, why stationary waves transfer no net energy, and the harmonic calculations on a fixed string — fundamental frequency from length and wave speed (the half-wavelength condition), and the third harmonic worked through the three-half-wavelengths geometry to 75 Hz.

Polarisation completes the set with both its conceptual and quantitative sides: a question — corrected during verification to be physically exact — establishing that polarisation and perpendicular oscillation are the properties genuinely exclusive to transverse waves (stationary waves and diffraction are not), and a Malus-law calculation through two polarising filters at 30°.

Each explanation shows the geometric reasoning, building the wavelength-fraction and string-harmonic pictures that exam diagrams assume.

• Apply the wave equation and period-frequency relationships with given values
• Convert path difference to phase difference, including beyond-2π results
• Explain stationary wave formation, node-antinode structure and in-phase regions
• Calculate harmonic frequencies for strings fixed at both ends
• Reason about polarisation as the signature of transverse waves, including Malus's law

Topic scope follows section 3.3.1 (Progressive and stationary waves) of the current A-level physics subject content: wave properties, phase and path difference, stationary waves, harmonics on strings, and polarisation.