Educator

Intro to Waves

• There are three main categories of waves:
  • Mechanical Waves: These travel through a material medium.
  • Electromagnetic Waves: EM waves do not require a material medium to exist.
  • Matter or Quantum Mechanical Waves: These describe the motion of elemental particles (electrons, protons, etc.) on the atomic level. We won't investigate them in this course.
• We also classify waves based on how they move:
  • Transverse Waves: The particles of the wave move perpendicular to the motion of the wave.
  • Longitudinal Waves: The particles of the wave move parallel to the motion of the wave. This is done through compression and rarefaction (expansion), i.e., the wave is transmitted by pressure changes.
• We describe a wave with the following characteristics:
  • Amplitude (A): How tall the wave is at its maximum height.
  • Wavelength (λ): The distance between "repeating" points on the wave, such as top-to-top.
  • Wave speed (v): How fast the wave is moving.
  • Period (T): The time it takes to go through a full oscillation.
  • Frequency (f): The number of oscillations that occur per second. [The unit for this is the hertz (Hz) where 1 Hz = [1/1s]. Thus, f = [1/T] and T = [1/f].]
• Because speed, frequency, and wavelength are all related, v = λf .
• We can find the height (or pressure differential if it's a longitudinal wave) with the following equation:
  

  y(x,t) = Asin(kx − ωt).

  • x is the horizontal location we are considering.
  • t is the time we are looking at the wave.
  • k is the angular wave number and is connected to the wavelength:
    

    k = 2π λ .

  • ω is the angular frequency and is connected to the period (which is connected to the frequency):
    

    ω = 2π T     ⇔     ω = 2π·f.