Units, prefixes and standard form
Convert prefixes, squared and cubed units. Write numbers in standard form.
Waves and interference questions
Calculate phase, fringe spacing and string harmonics; add wave displacements.
Practise
Add signed displacementsAt one point and instant, two transverse waves produce displacements +6 mm and -2 mm along the same axis. Find the signed resultant displacement. Give your answer to 3 significant figures.
Treat the given values as exact unless an uncertainty is stated.
Hint
Add the instantaneous displacements algebraically, not their amplitudes.
Worked solution
- y = 6 + (-2) = 4 mm.
- Answer: 4.00 mm (3 significant figures).
Question type: Mixed practice
Report a problem
A cycle in space and time
Wavelength is the distance for one complete spatial cycle; period is the time for one cycle. Use v = fλ and f = 1/T. For points on a progressive wave, phase-difference magnitude in degrees is 360° × separation/λ. These phase tasks use separations less than one wavelength and request a positive angle from 0° to 360°, including angles above 180°. They do not ask for the smaller equivalent angle or a signed phase lead.
Superposition and interference
Add instantaneous displacements with their signs. Coherent sources have a constant phase difference. For sources in phase, integer-wavelength path differences give constructive interference; half-integer differences give destructive interference. Complete cancellation also requires equal amplitudes at the observation point.
Fringes and stationary waves
Young’s double-slit formula w = λD/s gives adjacent bright-fringe spacing under the small-angle approximation. Keep wavelengths and distances in compatible units. Adjacent nodes of a stationary wave are λ/2 apart. A string fixed at both ends contains n half-wavelengths at harmonic n, so f = nv/(2L). Open and closed pipes, diffraction patterns and refraction are outside this resource’s scope.
A-level relevance
AQA 7408: 3.3.1.1–3, 3.3.2.2 (selected); OCR A H556: 4.4.1; 4.4.3–4 (selected). Tasks cover the selected skills listed above.