Physics - Waves

Waves transfer energy and information without transferring matter. They can be classified as mechanical (require a medium) or electromagnetic (can travel through a vacuum).

Transverse waves have oscillations perpendicular to the direction of energy transfer (e.g., light waves, water waves).

Longitudinal waves have oscillations parallel to the direction of energy transfer, consisting of compressions and rarefactions (e.g., sound waves).

Amplitude ($A$) is the maximum displacement from the rest position. Wavelength ($\lambda$) is the distance between two consecutive corresponding points (e.g., crest to crest).

Frequency ($f$) is the number of waves passing a point per second, measured in Hertz ($Hz$). The Period ($T$) is the time taken for one complete oscillation: $T = \frac{1}{f}$.

Reflection: The angle of incidence ($i$) is equal to the angle of reflection ($r$).

Refraction: The change in direction of a wave as it crosses a boundary between two different media due to a change in speed. When light enters a denser medium, it slows down and bends towards the normal.

Refractive Index ($n$): A measure of how much a medium slows down light. It is defined as $n = \frac{\sin i}{\sin r}$ or $n = \frac{c}{v}$.

Total Internal Reflection (TIR): Occurs when light travels from a more dense to a less dense medium and the angle of incidence is greater than the critical angle ($c$).

Diffraction: The spreading of waves as they pass through a gap or around an edge. Significant diffraction occurs when the gap size is similar to the wavelength ($\lambda$).

The Electromagnetic (EM) Spectrum consists of transverse waves traveling at $v = 3 \times 10^8 \text{ m/s}$ in a vacuum. Order (low to high frequency): Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma rays.

Sound waves: Longitudinal waves that require a medium. Human hearing range is $20 \text{ Hz}$ to $20,000 \text{ Hz}$ ($20 \text{ kHz}$). Sound travels faster in solids than in liquids, and faster in liquids than in gases.