Equation sheet

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	${\displaystyle p=IA}$		${\displaystyle I=\frac{p}{4\pi R^2}}$
${\displaystyle p_{ave}=2{\pi }^2{A}^2{f}^2\mu v}$	${\displaystyle v=f\lambda }$	${\displaystyle v=\frac{\omega }{k}}$	${\displaystyle \beta =10lo{g}_{10}\frac{I}{I_0}}$
${\displaystyle A_{trans}=\frac{2}{1+\frac{k_T}{k_I}}{A}_{inc}}$	${\displaystyle A_{ref}=\frac{1-\frac{k_T}{k_I}}{1+\frac{k_T}{k_I}}{A}_{inc}}$	${\displaystyle k=\frac{2\pi }{\lambda }}$	${\displaystyle \omega =2\pi f}$
${\displaystyle y(x,t)=A\sin [\frac{2\pi }{\lambda }(x-vt)]}$	${\displaystyle y(x,t)=A\sin [kx-\omega t]}$	${\displaystyle v_{str}=\sqrt{\frac{T}{\mu }}}$	${\displaystyle v_{sound}=c=\sqrt{\frac{\gamma P_0}{{\rho }_0}}}$
${\displaystyle P=P_0-P_0\gamma \frac{dy(x,t)}{dx}}$	${\displaystyle I_0=1.0\times 10^{-12}\frac{W}{m^2}}$	${\displaystyle \gamma =1.4}$	${\displaystyle c=343\frac{m}{s}}$
${\displaystyle {\rho }_0=1.4\frac{kg}{m^3}}$	${\displaystyle P_0=1.01\times 10^5\frac{N}{m^2}}$	${\displaystyle v_{med}=A\omega }$	${\displaystyle v_{med}=\frac{dy(x,t)}{dt}}$
${\displaystyle \Delta \beta =20{\log }_{10}\frac{r_2}{r_1}}$	${\displaystyle {\lambda }_{cl}=\frac{4L}{n}}$	${\displaystyle {\lambda }_{op}=\frac{2L}{n}}$	${\displaystyle \mu =\frac{m}{L}}$
${\displaystyle I=\frac{1}{2}\rho v{v}_{max}^2}$	${\displaystyle I=\frac{1}{2}\frac{\Delta P_{max}^2}{\rho v}}$	${\displaystyle f_n=\frac{n}{2L}\sqrt{\frac{T}{\mu }}}$	${\displaystyle r_1-r_2=(n+\frac{1}{2})\lambda }$

${\displaystyle F_{2,1}=\frac{q_1{q}_2(r_2-r_1)}{4\pi {\epsilon }_0\mid r_2-r_1{\mid }^3}}$	${\displaystyle \mid F_{2,1}\mid =\frac{\mid q_1{q}_2\mid }{4\pi {\epsilon }_0\mid r_2-r_1{\mid }^2}}$	${\displaystyle V\left(r\right)=\frac{q}{4\pi {\epsilon }_0\mid r\mid }}$	${\displaystyle k=\frac{1}{4\pi {\epsilon }_0}=9.0\times 10^9\frac{N{m}^2}{C^2}}$
${\displaystyle E_1=\frac{F_{2,1}}{q_2}}$	${\displaystyle \mid E\mid =\frac{q}{4\pi {\epsilon }_0{r}^2}}$	${\displaystyle \mid E\mid =\frac{\lambda }{2\pi {\epsilon }_{0}r}}$	${\displaystyle \mid E\mid =\frac{\sigma }{2{\epsilon }_0}}$
${\displaystyle V\left(r\right)=\frac{q}{4\pi {\epsilon }_{0}r}}$	${\displaystyle V\left(r\right)=\frac{-\lambda }{2\pi {\epsilon }_0}\ln \mid r\mid }$	${\displaystyle V\left(x\right)=V_0-\frac{\sigma x}{2{\epsilon }_0}}$	${\displaystyle \delta W=q\Delta V}$
${\displaystyle V\left(r_f\right)-V\left(r_i\right)=-{\int }_{r_i}^{r_f}E\cdot dr}$	${\displaystyle E_x=-\frac{\partial V}{\partial x}}$	${\displaystyle E=-\nabla V}$	${\displaystyle \frac{d}{dx}\frac{1}{\sqrt{x^2+y^2}}=-\frac{x}{\sqrt{(x^2+y^2{)}^3}}}$

			${\displaystyle \tan \theta =\frac{\sin \theta }{\cos \theta }}$
${\displaystyle \frac{d}{dx}{x}^n=n{x}^{n-1}}$	${\displaystyle \frac{d}{dx}\cos (ax)=-a\sin (ax)}$	${\displaystyle \frac{d}{dx}\sin (ax)=a\cos (ax)}$	${\displaystyle \int x^{n}dx=\frac{1}{n+1}{x}^{n+1}+c}$
${\displaystyle \frac{d}{dx}{\tan }^{-1}x=\frac{1}{1+x^2}}$	${\displaystyle \frac{d}{dx}uv=\frac{du}{dx}v+u\frac{dv}{dx}}$	${\displaystyle \frac{d}{dx}\frac{u}{v}=\frac{\frac{du}{dx}v-u\frac{dv}{dx}}{v^2}}$	${\displaystyle {\int }_a^{b}udv=\left(uv\right){:\mid :}_a^b-{\int }_a^{b}vdu}$
${\displaystyle \frac{d}{dx}{e}^{f\left(x\right)}=e^{f\left(x\right)}\frac{df\left(x\right)}{dx}}$	${\displaystyle \frac{d}{dx}\ln \mid x\mid =\frac{1}{x}}$	${\displaystyle {\int }_a^b\frac{df\left(x\right)}{dx}dx=f\left(b\right)-f\left(a\right)}$	${\displaystyle \frac{d}{dx}{\sin }^{-1}x=\frac{1}{\sqrt{1-x^2}}}$
${\displaystyle \tan (a-b)=}$	${\displaystyle \cos (a-b)=}$	${\displaystyle \sin (a-b)=}$
${\displaystyle \frac{\tan a-\tan b}{1+\tan a\tan b}}$	${\displaystyle \cos a\cos b+\sin a\sin b}$	${\displaystyle \sin a\cos b-\cos a\sin b}$	${\displaystyle {\int }_a^b\frac{dx}{(x+c{)}^2}=\frac{1}{a+c}-\frac{1}{b+c}}$

${\displaystyle \Delta \beta =10{\log }_{10}\left(2\right(1+\cos \phi \left)\right)}$

${\displaystyle \Delta \beta =10{\log }_{10}\frac{R_1^2}{R_2^2}}$

${\displaystyle f_n=n\frac{c}{2L}}$

${\displaystyle f_n=(2n+1)\frac{c}{4L}}$