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zNbmrqy}M$42VDR9ddnmFeW(3#Dro50raFqdE5D>4)nD$U$kw|sQOhD=P|elFe+{95 zKFp<&e|xs0RkDa=%fXg5qHu}(3{zN3;cv zq9}xjAi7pY@sZPeQSPgL0%ftD6?{M{q@>UyV`~*=E0FLVb5Rxz`rsog*%r(wX525v~@jhY(;2g<#z-KqE}DP*CO0~T3V zhEM9TIhkP}q(T%=?!nY6{OVXq_|K++b;5O^x#Z8X?xDZopa!d)d?kP)##c;a zaWD{}YWmExHL)vNCVaBi>JSKP%x>VvXvfT=-a z#6hBNT009k>c=-0XFinqeiX6SU&}niJ|TKntM2lpLpBS-3^y?)V2chNl=>!LmVsHm XmYeCGssB4lL + +## Longitudinal (motion $||$ wave) + +**rarefactions** (expansions) and **compressions** + +![](graphics/longitudinal-waves.png) + +## Transverse waves (motion $\perp$ wave) + +**nodes** are fixed on graph + +![](graphics/transverse-waves.png) + +## 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 + +![](graphics/polarisation.png){#id .class width=20%} + +## Refraction + + + +![](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 - $n_1 \sin \theta_1=n_2 \sin \theta_2$ + +## 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 ($=S_1-S_2$) + +![](graphics/em-spectrum.png){#id .class height=100px} \ No newline at end of file diff --git a/physics/waves-ref.pdf b/physics/waves-ref.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1b1fb9c0244ec2934808ed7e1363c286b762bc68 GIT binary patch literal 373717 zcmce-WmH_1*XRfu2;=70#9TPnpJjK*p{~|maBMBpkje!L`FE2cUjIp(;qZtV^ z7bh3VKY#EHV&;~P#`Yu(VwU=j#v;asHb%zq{QU3^j`qg-R`9ON?V3wbD?^xG4{C>W zpY`l4fCM<*w74?RaGQP5`}!tCMxkqT!nw=&%T^y=a#rNwIti;Rf_mAq3cpud9#$Qa zXIw6HJ#Wa!5NK%VF|^uRH6&E1N3nlNwtWtFY3;8X1*)pjascF#vsSZOwBFv&4;W)r zRiy-CY3H?7mk${avWoVdeY_XX(#G|F?`zWgki`+mAH0>o%{CLr7mcaH$4jQXZwZ^D z@G4Tyrigz<>@!fHwfxpgON!l48%E7xE(=wHXdDx*tbN7UyjFiVZgSEWI+$a@DygrO 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