wave motion

• Wave


  A disturbance that moves from one point to another
• Wave motion


  A regular rhythmic disturbance in both time and space, where the transfer of energy takes place
• The basic concept in interpreting the term 'wave' is that it involves some quantity or disturbance that changes in magnitude with respect to time at a given location and changes in magnitude from place to place at a given time
• Classification of waves


  • Mechanical waves
  • Electromagnetic waves
• Mechanical waves


  • Propagated in some material medium such as sound waves, water waves, waves on a stretched string, waves generated by earthquakes
• Types of mechanical waves

  • Transverse wave
  • Longitudinal or compressional wave
• Transverse wave


  Wave in which the individual particles move up and down at right angles to the direction in which the wave travels
• Parts of transverse wave

  • Crest
  • Trough
  • Amplitude
  • Wavelength
• Longitudinal or compressional wave


  Wave in which the individual particles vibrate back and forth along the direction in which the wave travels
• Parts of longitudinal wave

  • Compression or Condensation
  • Rarefactions
• Electromagnetic waves


  • Do not require a medium for their propagation such as radiowave, infrared, visible light, ultraviolet rays, microwave, X-rays, gamma – rays
• Properties of waves


  • Wave transfers energy and not matter
  • Wave transmits information
  • When more than one wave occurs in a medium, the overall disturbance is the sum of the individual disturbance
  • Whenever waves encounter an abrupt change in the medium reflections are produced
  • Most waves undergo refraction
• Parameters describing waves


  • Amplitude
  • Wavelength
  • Period
  • Frequency
  • Wave speed
• Amplitude


  The maximum height of a crest or depth of a trough relative to the normal (or equilibrium) level
• Wavelength


  The distance between two successive crests of a wave or two successive troughs or between two adjacent points in a wave train that have the same phase of vibration
• Period


  The time elapsed between two successive crests passing by the same point in space
• Frequency


  The number of crests or complete cycles that pass in each point per unit time
• Wave speed


  The speed in which wave crests moves through a medium. It depends on the kind of the wave produced and on the nature of the medium through which the wave moves. It is the product of the frequency of a wave and the wavelength
• The motion of the medium during the propagation of the continuous waves with a sinusoidal shape is simple harmonic motion
• Speed of transverse wave on a string

  v = √(FT/μ), where μ = m/L
• Speed of longitudinal wave

  v = √(Elasticity/Density)

  For solids: v = √(γ/ρs)

  For liquids and gases: v = √(β/ρ)
• Transverse wave speed


  v = √(FT/μ)
• Linear density


  μ = m/L
• Speed of longitudinal wave

  • Depends on an elastic property and on an inertial property (density) of a medium
• Speed of longitudinal wave in solids


  v = √(γ/ρs)
• Speed of longitudinal wave in liquids and gases

  v = √(β/ρ)
• Solving for transverse wave speed on a string

  1. Calculate linear density μ = m/L

  2. Use v = √(FT/μ) to find the wave speed
• A uniform string has a mass of 0.0300 kg and a length of 6.00 m. Tension (downward motion) is maintained in the string by suspending a block of mass 2.00 kg. Find the speed of a transverse wave pulse on the string.
• The speed of a compressional wave in a steel rod with Young's modulus of elasticity 2.4x10^11 N/m^2 and density 7.8 g/cm^3 is 550,000 m/s.
• Solving for transverse wave speed on a string with given tension and mass

  1. Calculate linear density μ = m/L

  2. Use v = √(FT/μ) to find the wave speed
• Solving for transverse wave speed on a wire with given tension and mass

  1. Calculate linear density μ = m/L

  2. Use v = √(FT/μ) to find the wave speed

  3. Repeat for doubled tension and doubled mass
• When a wave reaches a boundary of the medium, it will return along its original path of motion.
• Free end reflection


  Wave is reflected along the rope in the same direction it came from
• Fixed end reflection


  Pulse is inverted when it reflects off the boundary
• Law of reflection


  Angle of incidence = Angle of reflection
• Refraction


  Change of direction, or bending of waves when they move between mediums
• Law of refraction


  n1 sin(θ1) = n2 sin(θ2)
• Solving for angle of refraction when light enters ethanol

  Use n1 sin(θ1) = n2 sin(θ2) to find θ2
• Solving for angle of incidence when light travels from air into water

  Use n1 sin(θ1) = n2 sin(θ2) to find θ1
• Solving for index of refraction of an unknown material

  Use n1 sin(θ1) = n2 sin(θ2) to find n2