+\pagenumbering{gobble}
+
+\hypertarget{waves}{%
+\section{Waves}\label{waves}}
+
+\hypertarget{longitudinal-motion-wave}{%
+\subsection{\texorpdfstring{Longitudinal (motion \(||\)
+wave)}{Longitudinal (motion \textbar{}\textbar{} wave)}}\label{longitudinal-motion-wave}}
+
+\textbf{rarefactions} (expansions) and \textbf{compressions}
+
+\includegraphics{graphics/longitudinal-waves.png}
+
+\hypertarget{transverse-waves-motion-perp-wave}{%
+\subsection{\texorpdfstring{Transverse waves (motion \(\perp\)
+wave)}{Transverse waves (motion \textbackslash{}perp wave)}}\label{transverse-waves-motion-perp-wave}}
+
+\textbf{nodes} are fixed on graph
+
+\includegraphics{graphics/transverse-waves.png}
+
+\hypertarget{measuring-mechanical-waves}{%
+\subsection{Measuring mechanical
+waves}\label{measuring-mechanical-waves}}
+
+\textbf{Amplitude \(A\)} - max displacement from rest position\\
+\textbf{Wavelength \(\lambda\)} - \(x\) distance between \(y_1=y_2\)\\
+\textbf{Frequency \(f\)} - number of cycles (wavelengths) per second
+
+\(T={1 \over f}\quad\)(period: time for one cycle)\\
+\(v=f \lambda \quad\)(speed: displacement per second)
+
+\hypertarget{doppler-effect}{%
+\subsection{Doppler effect}\label{doppler-effect}}
+
+When \(P_1\) 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.
+
+\hypertarget{interference}{%
+\subsection{Interference}\label{interference}}
+
+When a medium changes character, energy is \emph{reflected},
+\emph{absorbed}, and \emph{transmitted}
+
+\textbf{Standing waves} - constructive int. at resonant freq
+
+\hypertarget{polarisation}{%
+\subsection{Polarisation}\label{polarisation}}
+
+\includegraphics[width=0.2\textwidth,height=\textheight]{graphics/polarisation.png}
+
+\hypertarget{refraction}{%
+\subsection{Refraction}\label{refraction}}
+
+\includegraphics{graphics/refraction.png}
+
+Angle of incidence \(\theta_i =\) angle of reflection \(\theta_r\)
+
+Critical angle \(\theta_c = \sin^-1{n_2 \over n_1}\)
+
+Snell's law - \(n_1 \sin \theta_1=n_2 \sin \theta_2\)
+
+\hypertarget{harmonics}{%
+\subsection{Harmonics}\label{harmonics}}
+
+where \(a=2\) for antinodes at both ends, \(a=4\) for antinodes at one
+end:
+
+\(\lambda = {{al} \div n}\quad\) (wavelength for \(n^{th}\) harmonic)\\
+\(f = {nv \div al}\quad\) (frequency for \(n_{th}\) harmonic at length
+\(l\) and speed \(v\))
+
+\hypertarget{double-split}{%
+\subsection{Double split}\label{double-split}}
+
+Path difference \(pd = |S_1P-S_2P|\) for point \(p\) on screen
+
+Constructive: \(pd = n\lambda\) where \(n \in [0, 1, 2, ...]\)\\
+Destructive: \(pd = (n-{1 \over 2})\lambda\) where
+\(n \in [1, 2, 3, ...]\)
+
+Fringe separation: \(\Delta x = {{\lambda l }\over d}\)
+
+where \(\Delta x\) is distance between fringes\\
+\(l\) is distance from slits to screen\\
+\(d\) is separation between sluts (\(=S_1-S_2\))
+
+\includegraphics[width=\textwidth,height=1.04167in]{graphics/em-spectrum.png}
