Properties of Waves - Part A

Introduction to Waves

• Waves are disturbances that transfer energy without the transfer of matter.

  

Types of Waves

1. Mechanical Waves

• Require a medium to travel (e.g., sound waves, water waves, and string waves).

  • Sound Waves: Produced by oscillations of particles in the medium.

  • String Waves: Produces by oscillations of the string elements.

  • Water Waves: Arise from the motion of water particles in the medium.

  

2. Electromagnetic Waves

• Do not require a medium; can travel through a vacuum.

• Generated by oscillations of electric and magnetic fields that are perpendicular to each other—travel perpendicular to both of the fields.

  

• Speed in Vacuum: All electromagnetic waves travel at a speed of 3 x10^8 m/s —fastest things in the universe.

• Electromagnetic Spectrum: The set of all electromagnetic waves arranged according to wavelength/frequency.

  

3. Matter Waves

• Associated with moving particles; exhibit wave behavior.

• Detectable only when the particle is very small and moves at high speed (e.g., electrons, protons, atoms and molecules).

  

• de Broglie's Equation:

• wavelength of the wave associated with the moving particle is given by:
  \lambda = \frac{h}{p}
  where h = 6.63 \times 10^{-34} J·s (Planck's constant) and p is momentum of the particle given by p = mv.

Wave Behavior

Longitudinal Waves

• Particle movement is parallel to the direction of wave/energy travel.

• Travel by creating compressions (high pressure) and rarefactions (low pressure).

  • Examples: Sound waves, certain seismic waves.

    

Transverse Waves

• Particle movement is perpendicular to the direction of wave/energy travel.

• Examples: String waves, water waves, light.

  

Wave Representation

• Waves can be represented using:

  • Displacement-Time Graphs: Shows how displacement varies with time.

  • Displacement-Distance Graphs: Shows how displacement varies with distance.

    

Wave Properties

• Time Period (T): Time taken to complete one cycle of oscillation.

• T= time/number of cycles (T=t/N)

• Frequency (f): Number of cycles completed in one second; measured in Hertz (Hz).

  • f = \frac{N}{t} where N is the number of cycles and t is the time.

• Pulse: The smallest part of a wave describing all properties.

• Amplitude: Maximum displacement from equilibrium position.

• Wavelength (λ): Distance between two corresponding points on the wave, measured in meters.

  

Wave Equations

• Wave Speed Equation: v = f \lambda

  • The speed of wave depends on the medium, not on frequency/wavelength.

• Example:

  • Speed of sound in air is different from the speed in water.

Example Problems

Special Scenarios