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### 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.

## Intro to Waves

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