Unit 9 (try 2)

• Oscillations


  • Repeating vibrations
• Angular speed (ω)


  Constant speed (Vo) and radius in uniform circular motion
• Angular speed (ω)


  Relates to period (T) and frequency (f)
• Frequency (f)


  Oscillations per second
• Period (T)


  Seconds per oscillation
• Simple Harmonic Motion (SHM)

  Defined by the equation a = -ω²x
• Oscillating spring


  Relates to uniform circular motion
• Equations of simple harmonic motion
• When mass begins at x = +xo at t=0s
• When mass begins at x = 0 at t=0s
• Formulas are highlighted in the data booklet
• Relation between displacement (x) and velocity (v) in SHM
• Mass-spring system undergoes SHM
• Period of mass-spring system
• Continuous exchange between potential energy and kinetic energy in SHM
• Mass on spring at end displaced 2.0 m undergoes SHM
• Total energy of 4.0 kg mass system
• Aperture


  Opening across an edge
• Huygens' principle


  • Every point on a wavefront emits a spherical wavelet of the same velocity and wavelength as the original wave
• This is why waves turn corners
• Diffraction effect


  The smaller the aperture, the more pronounced the diffraction effect
• The aperture size must be in the order of the wavelength
• Path difference


  The difference in distance travelled by two waves
• Path difference


  • b=62
  • b=27
• Bigger aperture


  Smaller path difference
• Smaller aperture


  Bigger path difference
• Coherent


  In phase and same frequency
• Path difference = nλ is the condition for constructive interference
• Path difference = (n+1/2)λ is the condition for destructive interference
• At first maximum, path difference is 0
• Huygens' principle


  • Each point on a wavefront emits a spherical wavelet of the same velocity and wavelength
• These wavelets interfere with each other
• At the central maximum, all wavelets travel the same distance, so constructive interference
• At the first minimum, the path difference is λ, causing destructive interference
• Intensity distribution in single-slit diffraction

  Caused by path length difference and interference
• The shape of the diffraction pattern depends on the ratio of slit width b to the wavelength λ
• The bigger the b, the closer the maxima and minima
• The smaller the λ, the closer the maxima and minima
• When white light is projected through a single slit, the central maxima is white, then the first maxima are purple, green, and red from closest to center
• Double slit interference


  Discovered by Thomas Young in 1801