Sound Waves

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.

Superposition of Waves

• 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.

Types of Mechanical Waves

• 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

• 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.

Simple Harmonic Motion (SHM)

• 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.

Sound Waves

• 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.

Superposition of Waves

• 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.

Types of Mechanical Waves

• 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

• 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.

Simple Harmonic Motion (SHM)

• 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.