physics / waves-ref.texon commit [methods] re-render methods notes (1dadb9e)
   1\pagenumbering{gobble}
   2
   3\hypertarget{waves}{%
   4\section{Waves}\label{waves}}
   5
   6\hypertarget{longitudinal-motion-wave}{%
   7\subsection{\texorpdfstring{Longitudinal (motion \(||\)
   8wave)}{Longitudinal (motion \textbar{}\textbar{} wave)}}\label{longitudinal-motion-wave}}
   9
  10\textbf{rarefactions} (expansions) and \textbf{compressions}
  11
  12\includegraphics{graphics/longitudinal-waves.png}
  13
  14\hypertarget{transverse-waves-motion-perp-wave}{%
  15\subsection{\texorpdfstring{Transverse waves (motion \(\perp\)
  16wave)}{Transverse waves (motion \textbackslash{}perp wave)}}\label{transverse-waves-motion-perp-wave}}
  17
  18\textbf{nodes} are fixed on graph
  19
  20\includegraphics{graphics/transverse-waves.png}
  21
  22\hypertarget{measuring-mechanical-waves}{%
  23\subsection{Measuring mechanical
  24waves}\label{measuring-mechanical-waves}}
  25
  26\textbf{Amplitude \(A\)} - max displacement from rest position\\
  27\textbf{Wavelength \(\lambda\)} - \(x\) distance between \(y_1=y_2\)\\
  28\textbf{Frequency \(f\)} - number of cycles (wavelengths) per second
  29
  30\(T={1 \over f}\quad\)(period: time for one cycle)\\
  31\(v=f \lambda \quad\)(speed: displacement per second)
  32
  33\hypertarget{doppler-effect}{%
  34\subsection{Doppler effect}\label{doppler-effect}}
  35
  36When \(P_1\) approaches \(P_2\), each wave \(w_n\) has slightly less
  37distance to travel than \(w_{n-1}\). Hence, \(w_n\) reaches the observer
  38sooner than \(w_{n-1}\), increasing ``apparent'' wavelength.
  39
  40\hypertarget{interference}{%
  41\subsection{Interference}\label{interference}}
  42
  43When a medium changes character, energy is \emph{reflected},
  44\emph{absorbed}, and \emph{transmitted}
  45
  46\textbf{Standing waves} - constructive int. at resonant freq
  47
  48\hypertarget{polarisation}{%
  49\subsection{Polarisation}\label{polarisation}}
  50
  51\includegraphics[width=0.2\textwidth,height=\textheight]{graphics/polarisation.png}
  52
  53\hypertarget{refraction}{%
  54\subsection{Refraction}\label{refraction}}
  55
  56\includegraphics{graphics/refraction.png}
  57
  58Angle of incidence \(\theta_i =\) angle of reflection \(\theta_r\)
  59
  60Critical angle \(\theta_c = \sin^-1{n_2 \over n_1}\)
  61
  62Snell's law - \(n_1 \sin \theta_1=n_2 \sin \theta_2\)
  63
  64\hypertarget{harmonics}{%
  65\subsection{Harmonics}\label{harmonics}}
  66
  67where \(a=2\) for antinodes at both ends, \(a=4\) for antinodes at one
  68end:
  69
  70\(\lambda = {{al} \div n}\quad\) (wavelength for \(n^{th}\) harmonic)\\
  71\(f = {nv \div al}\quad\) (frequency for \(n_{th}\) harmonic at length
  72\(l\) and speed \(v\))
  73
  74\hypertarget{double-split}{%
  75\subsection{Double split}\label{double-split}}
  76
  77Path difference \(pd = |S_1P-S_2P|\) for point \(p\) on screen
  78
  79Constructive: \(pd = n\lambda\) where \(n \in [0, 1, 2, ...]\)\\
  80Destructive: \(pd = (n-{1 \over 2})\lambda\) where
  81\(n \in [1, 2, 3, ...]\)
  82
  83Fringe separation: \(\Delta x = {{\lambda l }\over d}\)
  84
  85where \(\Delta x\) is distance between fringes\\
  86\(l\) is distance from slits to screen\\
  87\(d\) is separation between sluts (\(=S_1-S_2\))
  88
  89\includegraphics[width=\textwidth,height=1.04167in]{graphics/em-spectrum.png}