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
Path difference and cancellationTwo coherent sources emit waves in phase with equal amplitudes at the observation point. Their path difference is 2.5 wavelengths. What happens at this point?
Hint
A half-integer path difference gives antiphase arrival. Equal amplitudes are needed for complete cancellation.
Worked solution
- Rule: Destructive interference: the resultant amplitude is zero.
- 2.5 wavelengths corresponds to an odd multiple of 180°. Equal-amplitude displacements cancel at this point.
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.