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% Document Info
\author{Diana D (dianadavis)}
\pdfinfo{
  /Title (physics-20-waves.pdf)
  /Creator (Cheatography)
  /Author (Diana D (dianadavis))
  /Subject (Physics 20: Waves Cheat Sheet)
}

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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
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    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
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\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Physics 20: Waves Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Diana D (dianadavis)} via \textcolor{DarkBackground}{\uline{cheatography.com/134628/cs/27831/}}}
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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Diana D (dianadavis) \\
  \uline{cheatography.com/dianadavis} \\
  \end{tabulary}
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 17th May, 2021.\\
   Updated 17th May, 2021.\\
   Page {\thepage} of \pageref{LastPage}.
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  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
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\begin{document}
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\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{2.28942 cm} x{2.68758 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Formulas}}  \tn
% Row 0
\SetRowColor{LightBackground}
{\bf{ {\emph{l}} = {\emph{v}}Δ{\emph{t}} }} \{\{nobreak\}\} & Where {\emph{l}} is the pulse length, {\emph{v}} is the speed, and Δ{\emph{t}} is the time to create a complete pulse \tn 
% Row Count 5 (+ 5)
% Row 1
\SetRowColor{white}
{\emph{v}} = {\emph{f λ}} & Where {\emph{v}} is the speed, {\emph{f}} is the frequency in Hertz, and {\emph{ λ}} is the wavelength \tn 
% Row Count 9 (+ 4)
% Row 2
\SetRowColor{LightBackground}
{\bf{ {\emph{L}} = (1/2){\emph{ λ}} }} \{\{nobreak\}\} & Where {\emph{L}} is the length of each node and {\emph{ λ}} is the wavelength \tn 
% Row Count 13 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\SetRowColor{LightBackground}
\mymulticolumn{2}{x{5.377cm}}{{\bf{Bold}} formulae are not given on the Physics 20 formula sheet}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.18988 cm} x{2.78712 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{5.377cm}}{\bf\textcolor{white}{Definitions}}  \tn
% Row 0
\SetRowColor{LightBackground}
Wave & Travelling disturbance that carries energy \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Electromagnetic Waves \{\{noshy\}\} & Do not require a medium to travel (light) \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Mechanical Waves & Require a medium to travel (air, water, string, etc.) \tn 
% Row Count 7 (+ 3)
% Row 3
\SetRowColor{white}
Transverse Waves & The particles in the medium vibrate (or are displaced) perpendicular to the direction of motion of the wave \tn 
% Row Count 12 (+ 5)
% Row 4
\SetRowColor{LightBackground}
Longitudinal Waves & The particles in the medium vibrate parallel to the direction of motion of the wave \tn 
% Row Count 16 (+ 4)
% Row 5
\SetRowColor{white}
Constructive \{\{nl\}\} Interference & When waves in the same phase overlap, their amplitudes add together \tn 
% Row Count 20 (+ 4)
% Row 6
\SetRowColor{LightBackground}
Destructive \{\{nl\}\} Interference & When waves of different phases overlap, their amplitudes cancel \tn 
% Row Count 23 (+ 3)
% Row 7
\SetRowColor{white}
Nodes & Points of complete destructive interference \tn 
% Row Count 25 (+ 2)
% Row 8
\SetRowColor{LightBackground}
Antinodes & Points of complete constructive interference, largest amplitude \tn 
% Row Count 28 (+ 3)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Transverse Waves}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/dianadavis_1621263349_Transverse Waves.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Along the pulse, energy is stored in both elastic potential and kinetic energy \newline - At max displacement, PE is at max and KE is zero \newline - At equilibrium, KE is at max \newline  \newline The greater the amplitude, the greater the energy of the wave}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Longitudinal Waves}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/dianadavis_1621263379_Longitudinal Waves.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{1.04425 cm} x{1.08602 cm} x{1.37841 cm} p{0.66832 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{4}{x{5.377cm}}{\bf\textcolor{white}{Examples of Wave Types}}  \tn
% Row 0
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{\bf{Wave Type}} & {\bf{Example}} & {\bf{Origin}} & {\bf{Medium}} \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Water Wave & Wake of boat & Boat moving & Water \tn 
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% Row 2
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Sound Wave & Stereo & Speaker vibrates & Air \tn 
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\seqsplit{Mechanical} Wave & Bull whip & Arm whips & \seqsplit{Leather} \tn 
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% Row 4
\SetRowColor{LightBackground}
Seismic Wave & \seqsplit{Earthquake} & Shifting rock layers & Rock \tn 
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% Row 5
\SetRowColor{white}
Shock Wave & Atomic explosion & Nuclear fission & Air \tn 
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Light Wave & Room light & Hot filament & None \tn 
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\hhline{>{\arrayrulecolor{DarkBackground}}----}
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\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Wave Behaviour}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/dianadavis_1621267237_Wave Behaviours.jpeg}}} \tn 
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\mymulticolumn{1}{x{5.377cm}}{{\bf{Reflection:}} When a wave reflects, it exhibits a phase change (crest -\textgreater{} trough or vice-versa) \newline {\bf{Refraction:}} \newline {\bf{Diffraction:}} \newline {\bf{Interference:}}}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
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\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
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\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Standing Waves, Nodes \& Antinodes}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/dianadavis_1621268474_Nodes & Antinodes.png}}} \tn 
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\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Standing Waves:}} when 2 wave trains with the same amplitude and wavelength move through each other, the resulting interfering pattern results in a standing wave, it appears to be standing still in a constance position \newline - The frequencies at which standing waves exist are the natural or fundamental resonant frequency \newline  \newline {\bf{Nodes:}} points of complete destructive interference \newline {\bf{Antinodes:}} points of complete constructive interference}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Wave Behaviours: Reflection}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/dianadavis_1621267332_Reflection.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Reflection:}} straight waves "bounce" off a surface such that the outgoing angle (angle of reflection) or reflection wave equal the incoming angle (angle of incidence) or incident wave \newline  \newline Angles are measure from the normal line (line perpendicular to the surface) \newline  \newline {\bf{Wave Train:}} a series of waves linked together in phase (moving with identical motion) \newline  \newline Wave fronts are reflected by a barrier}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
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\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Wave Behaviours: Refraction}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/dianadavis_1621267406_Refraction.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{When a wave passes from one medium to another through a boundary, the waves bends and changes direction (and speed) at the interface \newline  \newline If the medium on the other side is 'thicker' (n), then the wave will slow down and bend towards the normal line}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Wave Behaviours: Diffraction}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/dianadavis_1621267969_Diffraction.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Diffraction:}} waves bend around a corner or opening \newline  \newline The amount of diffraction depends on the wavelength and the size of the opening \newline  \newline Waves lose amplitude, not speed or frequency}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Wave Behaviours: Interference}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/dianadavis_1621268065_Interference.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Constructive:}} "in phase" waves produce larger amplitudes \newline {\bf{Destructive:}} "out of phase" waves amplitudes cancel \newline  \newline {\bf{Principle of Superposition:}} the two waves "superimpose" and "interfere" with each other, creating a temporary waveform that is the sum of the two waves}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Doppler Effect}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/dianadavis_1621267269_Screen Shot 2021-05-17 at 9.03.29 AM.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{Fo = observers frequency \newline Fs = emitted frequency \newline V = speed of sound \newline Vs = speed of object emitting sound \newline  \newline Subtract when the {\bf{source is moving towards the observer}} \newline Add when the {\bf{source is moving away from the observer}}}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Doppler Effect Cont.}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{When the source is moving towards the observer with a velocity, the waves spread out in circles around the source, the frequency doesn't change but the waves crowd together, making the wavelength shorter. \newline % Row Count 5 (+ 5)
When the source is moving away from the observer, the wavelength is lengthened and the detected frequency is lower% Row Count 8 (+ 3)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Stringed Resonator}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/dianadavis_1621268727_Stringed Resonator.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Stringed Resonator:}} a resonating instrument that is fixed at both ends}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Closed-Pipe Resonator}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/dianadavis_1621268863_Closed-Tube Resonator.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Closed-Pipe Resonator:}} tube is closed at one end and open at another \newline  \newline In a closed-tube, node at closed end and either node or antinode at open end. \newline IF antinode occurs at the open end, resonance occurs and the sound is amplified (louder). \newline IF a node occurs at the open end, resonance does not occur and almost no sound (hence only odd harmonics)}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Open-Pipe Resonator}}  \tn
\SetRowColor{LightBackground}
\mymulticolumn{1}{p{5.377cm}}{\vspace{1px}\centerline{\includegraphics[width=5.1cm]{/web/www.cheatography.com/public/uploads/dianadavis_1621268805_Open-Tube Resonator.png}}} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\SetRowColor{LightBackground}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Open-Pipe Resonator:}} both ends of the tube are open}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Musical Instruments \& Resonance}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{{\bf{Fundamental/1st Harmonic:}} the lowest frequency making up the sound \newline % Row Count 2 (+ 2)
- Wave of frequencies that are whole number multiples of the fundamental are called harmonics (2nd, 3rd, 4th, etc)% Row Count 5 (+ 3)
} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}