physics / waves-ref.mdon commit [english] start Ransom & Invictus notes (b0fa307)
   1---
   2geometry: margin=2cm
   3columns: 2
   4graphics: yes
   5author: Andrew Lorimer
   6---
   7
   8\pagenumbering{gobble}
   9
  10# Waves
  11
  12<!-- **Nodes** are fixed on graph -->
  13<!-- **Crests** (peaks) & **troughs** (azimuths) -->
  14## Longitudinal (motion $||$ wave)
  15
  16**rarefactions** (expansions) and **compressions**
  17
  18![](graphics/longitudinal-waves.png)
  19
  20## Transverse waves (motion $\perp$ wave)
  21
  22**nodes** are fixed on graph
  23
  24![](graphics/transverse-waves.png)
  25
  26## Measuring mechanical waves
  27
  28**Amplitude $A$** - max displacement from rest position  
  29**Wavelength $\lambda$** - $x$ distance between $y_1=y_2$  
  30**Frequency $f$** - number of cycles (wavelengths) per second
  31
  32$T={1 \over f}\quad$(period: time for one cycle)  
  33$v=f \lambda \quad$(speed: displacement per second)
  34
  35## Doppler effect
  36When $P_1$ approaches $P_2$, each wave $w_n$ has slightly less distance to travel than $w_{n-1}$. Hence, $w_n$ reaches the observer sooner than $w_{n-1}$, increasing "apparent" wavelength.
  37
  38## Interference
  39
  40When a medium changes character, energy is _reflected_, _absorbed_, and _transmitted_
  41
  42**Standing waves** - constructive int. at resonant freq
  43
  44## Polarisation
  45
  46![](graphics/polarisation.png){#id .class width=20%}
  47
  48## Refraction
  49
  50<!-- ![](graphics/rays.png) -->
  51
  52![](graphics/refraction.png)
  53
  54Angle of incidence $\theta_i =$ angle of reflection $\theta_r$
  55
  56Critical angle $\theta_c = \sin^-1{n_2 \over n_1}$
  57
  58Snell's law - $n_1 \sin \theta_1=n_2 \sin \theta_2$
  59
  60## Harmonics
  61
  62where $a=2$ for antinodes at both ends, $a=4$ for antinodes at one end:
  63
  64$\lambda = {{al} \div n}\quad$ (wavelength for $n^{th}$ harmonic)  
  65$f = {nv \div al}\quad$ (frequency for $n_{th}$ harmonic at length $l$ and speed $v$)
  66
  67
  68## Double split
  69
  70Path difference $pd = |S_1P-S_2P|$ for point $p$ on screen
  71
  72Constructive: $pd = n\lambda$ where $n \in [0, 1, 2, ...]$  
  73Destructive: $pd = (n-{1 \over 2})\lambda$ where $n \in [1, 2, 3, ...]$
  74
  75Fringe separation: $\Delta x = {{\lambda l }\over d}$
  76
  77where
  78$\Delta x$ is distance between fringes  
  79$l$ is distance from slits to screen  
  80$d$ is separation between sluts ($=S_1-S_2$)
  81
  82![](graphics/em-spectrum.png){#id .class height=100px}