Waves

1. Types of Waves

  • Mechanical Waves: Require a medium to propagate.
    • Transverse Waves: Particle displacement is perpendicular to wave propagation (e.g., waves on a string, light waves).
      • Crucial for JEE: Understanding the relationship between wave speed, tension, and linear density (v = √(T/μ)).
    • Longitudinal Waves: Particle displacement is parallel to wave propagation (e.g., sound waves).
      • Crucial for JEE: Knowing the speed of sound in different media and how it’s affected by temperature and pressure (v = √(γP/ρ)).
  • Electromagnetic Waves: Do not require a medium; transverse in nature.
    • Crucial for JEE: Understanding the electromagnetic spectrum, properties of different types of EM waves, and their applications.
  • Matter Waves: Associated with moving particles (e.g., electrons).
    • Crucial for JEE: Understanding the de Broglie wavelength (λ = h/p) and its significance in quantum mechanics.

2. Wave Properties and Equations

  • Amplitude (A): Maximum displacement from equilibrium.
  • Wavelength (λ): Distance between two consecutive points in phase.
  • Frequency (f): Number of oscillations per unit time.
  • Period (T): Time for one complete oscillation. T = 1/f
  • Wave Speed (v): Speed of wave propagation. v = fλ
  • Wave Equation: Describes the motion of a wave. y(x,t) = A sin(kx – ωt + φ) (where k is the wave number, ω is the angular frequency, and φ is the phase constant).
    • Crucial for JEE: Applying this equation to analyze wave motion and solve problems.

3. Superposition and Interference

  • Superposition Principle: When two or more waves meet, the resultant displacement is the vector sum of individual displacements.
  • Interference: The combination of waves resulting in a new wave pattern.
    • Constructive Interference: Waves in phase add up, resulting in a larger amplitude.
    • Destructive Interference: Waves out of phase cancel out, resulting in a smaller amplitude.
    • Crucial for JEE: Analyzing interference patterns, calculating path differences, and understanding conditions for constructive and destructive interference.

4. Diffraction

  • Concept: The bending of waves around obstacles or through openings.
  • Single-slit diffraction: Produces a pattern of bright and dark fringes.
  • Diffraction grating: Multiple slits that produce a sharper interference pattern.
    • Crucial for JEE: Understanding the conditions for diffraction and analyzing diffraction patterns.

5. Doppler Effect

  • Concept: The change in frequency of a wave due to the relative motion between the source and the observer.
  • Applications: Radar guns, astronomy, medical imaging.
    • Crucial for JEE: Applying the Doppler effect formula to calculate the apparent frequency for different scenarios.

Formula Sheet