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
Harmonics on a stringA string of length 1 m is fixed at both ends. Wave speed is 250 m s⁻¹. Find the frequency of harmonic 4. Ignore changes in tension and end effects. Give your answer to 3 significant figures.
Larger diagram
Treat the given values as exact unless an uncertainty is stated.
Hint
There are n half-wavelengths in the string: λ = 2L/n, then f = v/λ.
Worked solution
- λ = 2 × 1/4 m.
- f = 4 × 250/(2 × 1) Hz.
- Answer: 500 Hz (3 significant figures).
Question type: Harmonics on a string
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.