Sound and Optics
This domain pairs the physics of sound with geometrical and physical optics. The exam tests speed of sound and resonance, beats and the Doppler effect, then reflection, refraction, total internal reflection, lenses and mirrors, and defects of vision.
Core rules
- Sound is longitudinal and requires a material medium; in air at room temperature it travels at roughly 330–340 m/s and rises by about 0.6 m/s for each degree Celsius. It travels faster in solids than in gases.
- Beats occur at f_beat = |f₁ − f₂|. Loading a tuning fork with wax lowers its frequency and increases the beat rate against a fixed fork.
- Resonance in a pipe closed at one end gives a fundamental f = v/4L; an open pipe gives f = v/2L. Real tubes need an end correction.
- Doppler shift: f′ = f(v ± v_observer)/(v ∓ v_source), with the signs chosen so approach raises the observed frequency.
- Reflection and refraction angles are always measured from the normal. Snell's law: n₁ sinθ₁ = n₂ sinθ₂, with n = c/v and sin C = 1/n for the critical angle.
- Using the real-is-positive convention: 1/f = 1/u + 1/v and magnification m = v/u = image height / object height.
- Total internal reflection requires travel from denser to less dense medium and an angle of incidence exceeding the critical angle.
- Myopia (short sight) is corrected with a diverging lens; hypermetropia with a converging lens.
Worked example
An object stands 30 cm from a converging lens of focal length 10 cm. Locate and describe the image. 1/v = 1/f − 1/u = 1/10 − 1/30 = 3/30 − 1/30 = 2/30, so v = +15 cm. The positive value means a real image on the far side; m = v/u = 15/30 = 0.5, so the image is inverted, real and half the object height.
Traps that cost marks
- Measuring angles from the lens or surface instead of the normal.
- Believing total internal reflection can occur going from air into glass.
- Mixing sign conventions part-way through a lens calculation, then mislabelling a virtual image as real.
- Assuming the frequency of light changes when it refracts.
- Ignoring the end correction in a resonance-tube experiment and reporting a speed that is systematically too low.
- Confusing beats (two close frequencies) with resonance (driven frequency matching natural frequency).