Sound Waves

Sound waves are mechanical waves that propagate through a medium (solid, liquid, or gas) and are perceived by the human ear as sound.
Characteristics:
- Longitudinal wave: particles oscillate back and forth along the direction of wave propagation.
- Frequency range: 20 Hz to 20,000 Hz (audible range).
- Speed: approximately 343 m/s in air at room temperature and atmospheric pressure.
Sound wave properties:
- Wavelength (λ): distance between two consecutive compressions or rarefactions.
- Frequency (f): number of oscillations per second.
- Amplitude (A): maximum displacement of particles from equilibrium.
- Period (T): time taken by one complete oscillation.

When two or more waves overlap in space and time, they superimpose to form a new wave.
Types of superposition:
- Constructive interference: waves add to form a wave with greater amplitude.
- Destructive interference: waves cancel each other out to form a wave with lesser amplitude.
Superposition principles:
- The amplitude of the resulting wave is the vector sum of the individual wave amplitudes.
- The frequency of the resulting wave is the same as the individual wave frequencies.

Transverse waves:
- Particles oscillate perpendicular to the direction of wave propagation.
- Examples: light waves, water waves.
Longitudinal waves:
- Particles oscillate along the direction of wave propagation.
- Examples: sound waves, seismic waves.
Mechanical waves can be classified based on their medium:
- Solid waves: propagate through solids (e.g., seismic waves).
- Liquid waves: propagate through liquids (e.g., water waves).
- Gas waves: propagate through gases (e.g., sound waves).

Damped oscillations occur when an oscillating system loses energy due to external forces (e.g., friction).
Characteristics:
- Amplitude decreases with time.
- Frequency remains constant.
Types of damping:
- Viscous damping: energy loss due to fluid resistance.
- Hysteresis damping: energy loss due to internal friction.
- Air resistance damping: energy loss due to air resistance.

SHM occurs when a particle oscillates about a fixed point in a sinusoidal manner.
Characteristics:
- Periodic motion with a constant period.
- Acceleration is proportional to displacement from the equilibrium position.
- Force is proportional to displacement from the equilibrium position.
SHM equations:
- Displacement: x(t) = A sin(ωt + φ)
- Velocity: v(t) = ωA cos(ωt + φ)
- Acceleration: a(t) = -ω^2A sin(ωt + φ)
- Where A is the amplitude, ω is the angular frequency, and φ is the phase angle.

Mechanical waves that propagate through a medium (solid, liquid, or gas) and are perceived by the human ear as sound.
Characteristics:
- Longitudinal wave: particles oscillate back and forth along the direction of wave propagation.
- Frequency range: 20 Hz to 20,000 Hz (audible range).
- Speed: approximately 343 m/s in air at room temperature and atmospheric pressure.

When two or more waves overlap in space and time, they superimpose to form a new wave.
Types of superposition:
- Constructive interference: waves add to form a wave with greater amplitude.
- Destructive interference: waves cancel each other out to form a wave with lesser amplitude.
Superposition principles:
- The amplitude of the resulting wave is the vector sum of the individual wave amplitudes.
- The frequency of the resulting wave is the same as the individual wave frequencies.

Transverse waves:
- Particles oscillate perpendicular to the direction of wave propagation.
- Examples: light waves, water waves.
Longitudinal waves:
- Particles oscillate along the direction of wave propagation.
- Examples: sound waves, seismic waves.
Mechanical waves can be classified based on their medium:
- Solid waves: propagate through solids (e.g., seismic waves).
- Liquid waves: propagate through liquids (e.g., water waves).
- Gas waves: propagate through gases (e.g., sound waves).

Damped oscillations occur when an oscillating system loses energy due to external forces (e.g., friction).
Characteristics:
- Amplitude decreases with time.
- Frequency remains constant.
Types of damping:
- Viscous damping: energy loss due to fluid resistance.
- Hysteresis damping: energy loss due to internal friction.
- Air resistance damping: energy loss due to air resistance.

SHM occurs when a particle oscillates about a fixed point in a sinusoidal manner.
Characteristics:
- Periodic motion with a constant period.
- Acceleration is proportional to displacement from the equilibrium position.
- Force is proportional to displacement from the equilibrium position.
SHM equations:
- Displacement: x(t) = A sin(ωt + φ)
- Velocity: v(t) = ωA cos(ωt + φ)
- Acceleration: a(t) = -ω^2A sin(ωt + φ)
- Where A is the amplitude, ω is the angular frequency, and φ is the phase angle.