Physics: Waves, Sound, and Light - Sound Waves, Hearing, Resonance, and Natural Frequency

Sound is a longitudinal wave produced by vibrations that requires a medium (solid, liquid, or gas) to travel through. It cannot travel through a vacuum.

Sound waves consist of Compressions (regions of high pressure where particles are close together) and Rarefactions (regions of low pressure where particles are spread out).

The speed of sound depends on the medium: it is fastest in solids and slowest in gases because particles in solids are more tightly packed, allowing vibrations to transfer more quickly ($v_{solid} > v_{liquid} > v_{gas}$).

Pitch is directly proportional to the frequency ($f$) of the wave. A higher frequency results in a higher pitch.

Loudness is determined by the amplitude ($A$) of the wave. A larger amplitude means more energy and a louder sound, typically measured in decibels ($dB$).

The human hearing range is typically between $20\text{ Hz}$ and $20,000\text{ Hz}$. Frequencies above this range are called ultrasound, and below are called infrasound.

Natural Frequency is the frequency at which an object tends to vibrate when disturbed. Resonance occurs when the frequency of an external periodic force matches the natural frequency of an object, leading to a dramatic increase in amplitude.

The Ear: The outer ear (pinna) collects sound, the middle ear (ossicles) amplifies it, and the inner ear (cochlea) converts vibrations into electrical signals for the brain.