--- /dev/null
+---
+geometry: margin=2cm
+columns: 2
+graphics: yes
+author: Andrew Lorimer
+---
+
+\pagenumbering{gobble}
+
+# Waves
+
+<!-- **Nodes** are fixed on graph -->
+<!-- **Crests** (peaks) & **troughs** (azimuths) -->
+## Longitudinal (motion $||$ wave)
+
+**rarefactions** (expansions) and **compressions**
+
+
+
+## Transverse waves (motion $\perp$ wave)
+
+**nodes** are fixed on graph
+
+
+
+## Measuring mechanical waves
+
+**Amplitude $A$** - max displacement from rest position
+**Wavelength $\lambda$** - $x$ distance between $y_1=y_2$
+**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)
+
+## 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.
+
+## Interference
+
+When a medium changes character, energy is _reflected_, _absorbed_, and _transmitted_
+
+**Standing waves** - constructive int. at resonant freq
+
+## Polarisation
+
+{#id .class width=20%}
+
+## Refraction
+
+<!--  -->
+
+
+
+Angle of incidence $\theta_i =$ angle of reflection $\theta_r$
+
+Critical angle $\theta_c = \sin^-1{n_2 \over n_1}$
+
+Snell's law - $n_1 \sin \theta_1=n_2 \sin \theta_2$
+
+## 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 $v$)
+
+
+## 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 ($=S_1-S_2$)
+
+{#id .class height=100px}
\ No newline at end of file
