mechanical wave

• Mechanical wave


  A periodic disturbance that travels through matter or space and transfers energy, not matter, from one location to another
• Longitudinal wave


  A wave where the particle displacement is parallel to the direction of wave propagation
• Transverse wave


  A wave where the particle displacement is perpendicular to the direction of wave propagation
• Periodic wave


  A wave where each particle in the medium experiences periodic motion as the wave travels through it
• Sinusoidal wave


  A periodic wave that is in simple harmonic motion
• Waves transport energy, not matter
• Medium


  The matter through which mechanical waves travel
• Types of mechanical waves


  • Longitudinal waves
  • Transverse waves
• Transverse waves


  • Particle displacement is perpendicular to the direction of wave propagation
  • Particles oscillate up and down about their equilibrium positions
• Examples of transverse waves


  • Ripples on water surface
  • Waves on guitar strings
  • Secondary earthquake waves
  • Stadium/human wave
  • Ocean waves
• Longitudinal waves


  • Particle displacement is parallel to the direction of wave propagation
  • Particles oscillate back and forth about their equilibrium positions
• Examples of longitudinal waves


  • Sound waves in air
  • Primary earthquake waves
  • Ultrasound
  • Spring vibrations
  • Gas fluctuations
  • Tsunami waves
• Sound waves can travel through solids, liquids, and gases
• Sound waves travel fastest through solids because the particles are closer together
• Examples of sound waves traveling through solids


  • Vibration of guitar strings
  • Vibration of saxophone reed
  • Vibration of piano soundboard
• Reflection


  When waves bounce off a surface, the angle of incidence equals the angle of reflection
• Refraction


  When a wave enters a new medium and its speed changes, causing the wave to bend
• Diffraction


  The bending of waves around an obstacle, depends on the size of the obstacle and the size of the waves
• Standing wave


  A wave that is reflected back upon itself, resulting in areas of maximum amplitude (antinodes) and zero amplitude (nodes)
• A periodic wave in simple harmonic motion is a sinusoidal wave
• Parts of a transverse wave


  • Crest (highest point)
  • Trough (lowest point)
  • Equilibrium position
• Parts of a longitudinal wave


  • Compression (high pressure, high density)
  • Rarefaction (low pressure, low density)
• Amplitude


  The maximum displacement of a particle from the equilibrium position
• Wavelength


  The distance between two successive crests or troughs
• Frequency


  The number of waves that pass a point per second
• Period


  The time required for one complete wave to pass a point
• Wave number


  A measure of the number of waves per unit distance
• Finding the Characteristics of a Sinusoidal Wave


  1. Write down the wave function in the form y(x,t) = Asin(kx - ωt + φ)

  2. Determine the phase constant φ based on initial conditions

  3. Find the amplitude A

  4. Derive the period T from the angular frequency ω

  5. Use ω = 2πf to get the frequency f

  6. Find the wave number k

  7. Derive the wavelength λ from the wave number

  8. Calculate the speed v = λ/T
• Phase constant φ


  Determines how displaced a wave is from an equilibrium or zero position
• For a mathematical wave, the phase constant tells you how displaced a wave is from an equilibrium or zero position
• Sinusoidal wave


  • Amplitude
  • Wavelength
  • Period
  • Frequency
  • Speed
  • Direction
  • Wave number
• The wave function in the form y(x,t) = Asin(kx - ωt + φ) contains all the characteristics of a sinusoidal wave
• Steps in Finding the Characteristics of a Sinusoidal Wave


  1. Write down the wave function

  2. Determine the phase constant φ

  3. Find the amplitude A

  4. Derive the period T from the angular frequency ω

  5. Use ω = 2πf to get the frequency f

  6. Find the wave number k

  7. Derive the wavelength λ from the wave number

  8. Calculate the speed v = λ/T
• The wave number k is the number of waves or cycles per unit distance
• The wavelength λ can be derived from the wave number
• The speed v of the wave is one wavelength per period
• Speed or Velocity of a Wave

  How fast the disturbance of the wave is moving, depends on the medium the wave is traveling through
• The principle of superposition states that when two or more waves meet at a point, the resultant displacement is equal to the sum of the displacements of the individual waves
• Interference


  When one wave comes into contact with another wave
• Interference


  • Constructive interference (higher amplitude)
  • Destructive interference (lower amplitude)