Waves, Sound and Optics
Waves, sound and optics: energy and information
A wave transfers energy without transferring matter. Transverse waves vibrate at right angles to the direction of travel; longitudinal waves vibrate parallel to it. Define amplitude, wavelength, frequency and period. The wave equation is v = fλ, where v is wave speed, f frequency in hertz and λ wavelength in metres. Frequency is set by the source and does not change when a wave enters a new medium; speed and wavelength do.
Reflection follows the law: angle of incidence equals angle of reflection, both measured from the normal. Refraction occurs because wave speed changes at a boundary; light bending towards the normal enters a denser medium. Refractive index n = sin i / sin r = c/v. When light travels from a denser to a less dense medium, total internal reflection occurs beyond the critical angle, where sin c = 1/n.
Lenses: a converging lens brings parallel rays to a principal focus; a diverging lens spreads them. Ray diagrams use standard rays. A real image can be projected on a screen and is inverted; a virtual image cannot. Sound is longitudinal, needs a medium, and travels faster in solids than gases. Pitch depends on frequency; loudness depends on amplitude. Echoes are reflected sound; ultrasound has frequency above 20 kHz.
Traps: measuring angles from the surface rather than the normal; assuming frequency changes on refraction; labelling a virtual image as real; saying sound travels through a vacuum; and confusing focal length with image distance.
Worked example: A sound wave of frequency 170 Hz travels at 340 m/s. λ = v/f = 340/170 = 2.0 m. For glass of refractive index 1.5, the critical angle is sin⁻¹(1/1.5) ≈ 41.8°.