Waves, Sound, and Optics
Waves, Sound, and Optics
This domain covers wave properties, superposition, standing waves, sound intensity and Doppler shift, reflection and refraction, lenses and mirrors, and interference. Expect quantitative items on the wave equation, Snell's law, and thin-lens or mirror equations.
Core rules
- Wave speed v = fλ. Frequency is set by the source and does not change when a wave enters a new medium; speed and wavelength change.
- Standing waves on a string fixed at both ends: f_n = nv/(2L). For a pipe open at both ends, f_n = nv/(2L); for one closed end, only odd harmonics occur: f_n = nv/(4L).
- Sound intensity level β = 10 log(I/I₀), with I₀ = 10⁻¹² W/m². Each 10 dB increase is a factor of 10 in intensity.
- Refraction: n₁ sinθ₁ = n₂ sinθ₂, with angles measured from the normal. Total internal reflection occurs above the critical angle sinθ_c = n₂/n₁ when n₁ > n₂.
- Thin lens or mirror: 1/f = 1/d_o + 1/d_i and magnification m = −d_i/d_o. A real image from a single lens is inverted; a virtual image is upright.
Worked example
An object is 15 cm from a converging lens with f = 10 cm. Use 1/f = 1/d_o + 1/d_i: 1/10 = 1/15 + 1/d_i, so 1/d_i = 1/10 − 1/15 = 1/30, giving d_i = 30 cm. The positive image distance means a real image on the opposite side. Magnification m = −30/15 = −2.0: the image is twice as tall and inverted.
Traps
- Measuring refraction angles from the surface instead of the normal.
- Assuming frequency changes when light enters glass; it does not.
- Mixing the sign conventions for virtual images and diverging lenses.
- Treating a node as maximum motion; it is a displacement minimum.