Understanding Oscillatory Motion and Wave Phenomena

Posted on Nov 19, 2024 in Physics

Simple Harmonic Motion (SHM)

Simple harmonic motion is a straight-line oscillatory motion where the restoring force is proportional to the displacement and acts in the opposite direction. Key features include:

  • Oscillation/Vibration
  • Oscillation Center (O)
  • Elongation (X)
  • Amplitude (A) – always positive
  • Period (T)
  • Frequency (F) = 1/T
  • Angular Frequency (ω)

Dynamics of SHM

-k: Restoring force constant
-F: Central force, proportional to displacement (r)
-T: Period depends on mass (m) and k, not amplitude (A)

Waves

A wave is a disturbance propagating through a medium, transporting energy without net matter transport.

Classifications

1. Mechanical Waves: Require a medium (elastic material) for propagation.
Electromagnetic Waves: Do not require a medium, propagate through oscillating fields (light, radio waves).

2. Transverse Waves: Vibration direction is perpendicular to propagation direction.
Longitudinal Waves: Vibration direction is parallel to propagation direction (sound).

Concepts

  • Focus: Point of disturbance initiation
  • Pulse Wave: Instantaneous disturbance
  • Wave Train: Continuous disturbance
  • Wave Front: Locus of points with the same phase
  • Ray: Direction perpendicular to the wave front

Harmonic Waves

Harmonic waves originate from periodic disturbances in an elastic medium due to SHM.

  • Position (x): Location of a point in the medium
  • Elongation (y): Displacement from equilibrium
  • Amplitude (A): Maximum elongation
  • Wavelength: Distance between two successive points in the same phase
  • Period (T): Time for one wavelength to pass
  • Frequency (f): Number of waves passing a point per unit time
  • Velocity of Propagation: Speed of wave propagation

Energy of a Harmonic Wave

Energy is distributed throughout the medium. Intensity is the energy passing through a unit area per unit time. For spherical waves, intensity is inversely proportional to the square of the distance from the focus.

Damping of a Wave

Damping is the decrease in amplitude due to:

  1. Distance: Energy spreads over a larger area.
  2. Absorption: Energy loss due to friction in the medium.

Basic Wave Phenomena

Wave Front: Surface of points vibrating in phase.
Rays: Lines indicating propagation direction, normal to wave fronts.
Plane Wave: Distant spherical wave fronts appear planar.

Huygens’ Principle

Each point on a wave front acts as a source of secondary wavelets.

Diffraction

Bending of waves around obstacles or through openings.

Reflection

Waves bouncing off a surface. Laws of Reflection:

  1. Incident ray, normal, and reflected ray are coplanar.
  2. Angle of incidence equals angle of reflection.

Refraction

Waves bending when passing from one medium to another. Laws of Refraction (Snell’s Law):

  1. Refracted ray, normal, and incident ray are coplanar.
  2. Ratio of sines of angles is constant, related to wave speeds.

Wave Interference

Superposition of two or more waves. Principle of Superposition: Displacement is the sum of individual wave displacements.

  • Constructive Interference: Increased amplitude.
  • Destructive Interference: Decreased amplitude.

Nodes: Points of zero amplitude.
Antinodes: Points of maximum amplitude.

Sound

Sound is a pressure disturbance propagating as a longitudinal wave. Audible range: 20 Hz to 20,000 Hz.

Qualities of Sound

  • Intensity: Related to amplitude.
  • Pitch: Related to frequency.
  • Timbre: Quality distinguishing sounds of the same pitch and intensity.

Loudness: Subjective perception of sound intensity.
Noise: Unwanted sound.

Light

Historical Evolution

  • Huygens: Wave theory.
  • Newton: Corpuscular theory.
  • Young, Fresnel: Interference and diffraction.
  • Maxwell: Electromagnetic theory.
  • Einstein: Photoelectric effect, photons.

Dual Nature: Wave-particle duality.