\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}