Waves & optics

Waves transfer energy without moving matter overall. Transverse waves vibrate at right angles to travel (light); longitudinal waves vibrate along it, with compressions and rarefactions (sound). Key terms: amplitude, wavelength ($\lambda$), frequency ($f$) and period ($T$).

$f=\frac{1}{T}$ and the wave equation $v=f\lambda$.

Waves reflect (angle of incidence = angle of reflection) and refract (change direction when their speed changes at a boundary). Slowing down bends a ray towards the normal; speeding up bends it away. Refraction changes speed and wavelength but not frequency. A moving source produces the Doppler effect, shifting the observed frequency.

Sound is a longitudinal wave made by a vibrating source and needs a medium. Louder = bigger amplitude; higher pitch = higher frequency. Reflections cause echoes. Human hearing spans $20\text{ Hz}$ to $20\text{ kHz}$; above that is ultrasound, used in sonar and medical scanning.

All EM waves are transverse and travel at the speed of light in a vacuum. In order of decreasing wavelength (increasing frequency): radio, microwave, infrared, visible, ultraviolet, X-rays, gamma. Higher-frequency waves carry more energy and can be more hazardous.

• Thinking waves carry matter along (they transfer energy only).
• Saying refraction changes frequency (it changes speed and wavelength).
• Getting the spectrum order reversed: radio is long wavelength, gamma short.