Waves, Optics and Sound
Waves, optics and sound tests wave behaviour, ray diagrams and resonance. Expect calculations on the wave equation, refraction, lenses and stationary waves.
Wave basics
v = fλ; frequency is set by the source and does not change on refraction, while speed and wavelength do. Transverse waves oscillate perpendicular to the direction of travel; longitudinal waves oscillate parallel to it. Intensity is proportional to amplitude squared.
Light: reflection and refraction
Snell's law: n₁ sinθ₁ = n₂ sinθ₂. Refractive index n = c/v. Total internal reflection occurs when light travels from a denser to a less dense medium and the angle exceeds the critical angle, sin c = n₂/n₁. For a thin lens, 1/f = 1/v + 1/u using the real-is-positive convention, and magnification m = v/u.
Sound and stationary waves
Sound is longitudinal and needs a medium. A resonance tube closed at one end gives odd harmonics: f = v/4L, 3v/4L, 5v/4L; a pipe open at both ends gives all harmonics: f = v/2L. Two-source interference gives maxima where path difference = nλ and minima where it is (n + ½)λ.
Worked example
An object is 30 cm from a converging lens of focal length 10 cm. 1/v = 1/f − 1/u = 1/10 − 1/30 = 2/30, so v = 15 cm. The image is real, inverted and diminished, with m = 15/30 = 0.5.
Traps
Mixing up u and v, forgetting the sign convention, and using the wrong end-correction in resonance-tube calculations.