Mod 3: Thermodynamics and waves

• Electromagnetic waves do not need a medium, since they are self propagating, meanwhile, mechanical waves need a medium to propagate theough
• A wave is a transfer of energy, not particles
• Longitudinal wave, particles are displaced parallel to wave propagation
• Transverse wave, particles are displaced perpendicular to wave propagation
• Wave behaviours include:

  Refraction

  Reflection

  Diffraction

  Superposition Auperpos
• Frequency: measured in Hertz (Hz) and it means how many wavelengths pass in a second
• Period: measured in seconds, the time for a complete wavelength to pass
• Frequency and period are inversely proportional
• Wave equation


  v(m/s)=f(Hz)λ(m)
• Wave behaviour:

  Refraction

  Reflection

  DIffraction

  Interference/superposition

  Standing and passing waves

  Resonance

  Harmonics (closed-closed, closed-open, open-open) for sound waves

  Doppler effect
• Reflection is when a wave is bounced from a boundary, you calculate this bouncing angle from the normal line (90°). The angle from the incident to reflected ray stays the same.

  
• The smoother the surface, the more reflective it usually is, since there are less small bumps along it, making the light rays disperse less
• Refraction occurs when a wave enters a different medium. This means that there is a change in wavelength and velocity
• The angle from the refracted ray shouldn't equal the angle of the incident ray under refraction

  
• Diffraction occurs when a wave escapes from a barrier with a gap in it. The smaller the gap, the more it will diffract. This gap shouldn't be smaller than the wavelength of the wave or else the wave will not pass.

  
• interference occurs when two waves collide together as time moves, either subtracting or adding the amplitudes. Amplitudes add if waves are in phase/similar to in phase and vice versa for completely off phase waves.
• Standing waves occur when waves are completely reflected from an unmoving surface which result in a series of nodes and antinodes. Through interference, these waves either get cancelled or added out as time continues.
• Passing waves occur when the end of the waves are able to move freely and not reflect
• When the natural frequency of an body interferes with the disturbed frequency caused by another wave, the amplitudes add up, creating a much higher amplitude, thus, a resonant frequency.
• n=c/v where 

  n=refractive index

  c=speed of light
• Harmonics are for standing waves where it is either:

  • two closed ends
  • one open end
  • two open ends
• To convert from harmonic to wavelength (for two closed and two open ends):

  1/harmonic * 2
• To convert from harmonic to wavelength (for one closed end):

  1/harmonic * 4
• Cannot hae an even number of harmonics in one open and one closed ends
• Each harmonic in one open and one closed end is from peak to crest, meanwhile, each harmonic in two open/closed ends are from antinodes to antinodes/nodes to nodes.
• Complete internal reflection occurs at the critical angle.
• Internal reflection is when the refracted ray is more than or equal to 90 degrees. This occurs when the wave is moving from a slower medium to a faster medium.
• To find the critical angle, Snell's law is used. Critical angle = sin-1(n2/n1) where n2 is the lighter medium (in which the wave travels faster in).
• Snell's law:

  n1*sinθ1 = n2*sinθ2
• Refractive index =n=c/v

  c = speed of wave in vacuum

  v = speed of wave in medium
• Inverse square law = 1/r^2, which is used to find the intensity of a wave.
• During a moving standing wave (while it is in full amplitude adding superposition), when there is a phase shift of even 1/4 of a period, the whole wave will deplete itself due to superposition. The resultant wave will be a straight line for a short period of time. This is also due to an anti-node shift from a node.
• diffraction affects the amplitude and direction of the wave
• λ<<d, no diffraction

  λ<d, some diffraction

  λ = d, most diffraction

  λ>d, no diffraction
• destructive interference: when the superposition of the waves end up in a lesser amplitude.

  constructive interference: when the superposition of the waves end up in a higher amplitude.
• For inverse square law questions with multiple variables:

  I₁*r₁² = I₂*r₂²
• n₁v₁ = n₂v₂, or c₁ = c₂
• v₁/v₂ = sin1/sinr = n₂/n₁ =  λ₁/λ₂