Waves and Sound Study Notes

Definition of Wave: A wave is a repeating disturbance or movement that transfers energy through space; it does not carry matter but carries energy.
- Matter vibrates as energy in a wave passes through.

Mechanical Waves: Require a medium (solid, liquid, gas) to travel. Governed by Newton’s laws.
- Examples: Earthquake waves (solids), ocean waves (liquids), and sound waves (gases).
Electromagnetic Waves: Do not require a medium; travel at the speed of light (approximately $3.00 imes 10^8 ext{ m/s}$ in a vacuum).
- Examples: Light, X-rays, radio waves, microwaves.
Matter Waves: Subatomic particles exhibiting wavelike properties, explained by quantum mechanics.

Types of Mechanical Waves:
- Compressional (Longitudinal) Waves: Energy is carried parallel to the direction of medium vibration (e.g., sound waves).
- Transverse Waves: Energy is carried perpendicular to the direction of medium vibration (e.g., vibrating guitar string).
Surface Waves: Combination of transverse and longitudinal waves, where the medium moves in circles (e.g., water waves, seismic waves).

Transverse Waves:
- Crest: Highest point of the wave.
- Trough: Lowest point of the wave.
- Amplitude: Height of crest or trough above or below the equilibrium position.
- Wavelength: Distance between two crests or troughs.
Longitudinal Waves:
- Compression: Region where particles are close together.
- Rarefaction: Region where particles are spread apart.
- Wavelength: Distance between consecutive compressions or rarefactions.
Frequency (f): Number of wave crests or troughs passing a point per second. Unit: Hertz (Hz).
- 1 ext{ Hz} = 1 ext{ wave per second}
Time Period (T): Time taken for one complete wave to pass a certain point.
- T = rac{1}{f}
Wave Velocity (v):
- Depends on the medium.
- v = ext{wavelength} imes f

Reflection: Bouncing back of a wave when it strikes a surface.
- Incident Wave: Wave striking a boundary.
- Reflected Wave: Wave that comes back from the boundary.
- Law of Reflection: The angle of incidence equals the angle of reflection.
Refraction: Bending of a wave as it enters a different medium, affecting speed, but not frequency.
Diffraction: Bending of waves around obstacles or through openings.
Interference: Occurs when two or more waves superimpose, resulting in constructive or destructive interference.
- Constructive Interference: Waves in phase create a wave with larger amplitude.
- Destructive Interference: Waves out of phase create a wave with smaller amplitude.

Formed from the interference of two waves traveling in opposite directions, creating nodes and antinodes.
- Nodes: Points of destructive interference where minimal movement occurs.
- Antinodes: Points of constructive interference where maximum movement occurs.

Occurs when an object vibrates at its natural frequency due to external energy absorption. Amplifies sound in musical instruments.

Sound is created by vibrating objects and travels as compressional waves.
- Speed of Sound: Varies with medium and temperature
- Slowest in gases, fastest in solids.
- Approximate speeds in air: $331 ext{ m/s}$ at $0^{ ext{°C}}$, $343 ext{ m/s}$ at $20^{ ext{°C}}$.

Intensity: Amount of energy carried by a sound wave, proportional to its amplitude.
- Intensity decreases with distance from the source.
- Measured in decibels (dB):
- $0 ext{ dB}$: quietest sound detectable.
- $120 ext{ dB}$: loudest sound detectable.
- Formula: eta = 10 imes ext{log} rac{I}{I0}, where $I0 = 1 imes 10^{-12} ext{ W/m}^2$.

Pitch: Determined by frequency; humans can hear frequencies from $20 ext{ Hz}$ to $20,000 ext{ Hz}$.
- Infrasonic: Frequencies below $20 ext{ Hz}$; Ultrasonic: Frequencies above $20,000 ext{ Hz}$.

Apparent change in frequency/pitch of a sound due to the motion of the source or observer.
- Approaching source: higher frequency; receding source: lower frequency.