view Lectures/Lec1 - Physics of Sound/Lec1 - Physics of Sound.tex @ 17:898873c7bb2b tip

This time?

\documentclass[handout]{beamer}

\usepackage{../C4DMlecturetheme}

\usecolortheme{beaver}

% Set up the lecture details here
\setlecturedetails
%COURSE DETAILS:
	{Sound Recording and Production} % COURSE TITLE
	{ECS614U/ECS749P} % COURSE CODE
%
%LECTURER DETAILS:
	{Michael Terrell} % LECTURER NAME(s)
	{[e-mail]} % LECTURER EMAIL(s)
	{http://qmplus.qmul.ac.uk/course/view.php?id=3243} % COURSE WEBPAGE URL
%
%LECTURE DETAILS:
	{1} % LECTURE NUMBER
	{The Physics of Sound} % LECTURE TITLE


\institute[C4DM]%
{Centre for Digital Music\\
School of Electronic Engineering and Computer Science\\
Queen Mary University of London}

\date[Semester 1, 2013--14]{Semester 1, 2013--14}

%\pgfdeclareimage[height=5mm]{theLogo}{QMULlogo}
%\logo{\pgfuseimage{theLogo}}

\beamerdefaultoverlayspecification{<+->}


\begin{document}
\section{Lecture \lecturenumber}
\subsection{ \lecturetitle}
\maketitle


\separator{Course Overview}

\begin{frame}
	\frametitle{Lectures}
	{\small
	\begin{columns}
	
	\column{4.5cm}
	\begin{enumerate}
		\item The Physics of Sound.
		\item Microphones.
		\item The Audio Chain.
		\item MIDI.
		\item Sound Design.
		\item Mixing: Gain.
	\end{enumerate}
		
		
	\column{4.5cm}
	\begin{enumerate}\setcounter{enumi}{6}
		\item Mixing: Delay.
		\item Mixing: Dynamics.
		\item Sound Reproduction.
		\item Psychoacoustics.
		\item Mastering.
		\item 
	\end{enumerate}
	
	\end{columns}
	}
	
\end{frame}

\begin{frame}
	\frametitle{Coursework}
	\begin{enumerate}\itemsep12pt
		\item Microphone project: {\bf 5\%} (11/10/2013).
		\item Apple loops project: {\bf 10\%} (1/11/2013).
		\item Soundscape concept document: {\bf 30\%} (22/11/2013).
		\item Soundscape audio and technical document: {\bf 55\%} (13/12/2013).
	\end{enumerate}
\end{frame}

\separator{The Physics of Sound}

\begin{frame}
	\frametitle{What is a sound?}
	\begin{itemize}\itemsep8pt
		\item A sound is a pressure wave.
		\item The pressure wave travels through an acoustic medium, i.e. air.
		\item The pressure wave consisting of compression and rarefaction.
		\item In the compression and rarefaction parts of the wave, the particles which form the acoustic medium are respectively squashed together and pulled apart.
		\item \href{http://illuminations.nctm.org/ActivityDetail.aspx?id=37}{\textit{Vibrating string animation}.}
	\end{itemize}
\end{frame}

\begin{frame}
	\frametitle{The waveform}
	\begin{itemize}\itemsep12pt
		\item A waveform is a graphical representation of a sound wave.
	\end{itemize}
	\begin{center}
		\includegraphics[width = 0.9  \textwidth]{Figures/waveform.pdf}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{The waveform}
	\begin{itemize}
		\item A waveform plot can represent one of two things:
		\setlength{\parskip}{0.25cm}
		\begin{enumerate}\itemsep8pt
			\item The waveform at a given point in space as it changes with time.
			\item The waveform at a given moment in time as it changes in space.
		\end{enumerate}
		\item \href{http://www.kettering.edu/physics/drussell/Demos.html}{\textit{Waves in space and time}.}
		\item When listening to a sound we are sensing the changes in pressure with time.
	\end{itemize}
\end{frame}

\begin{frame}
	\frametitle{Sound wave properties}
	\begin{itemize}\itemsep12pt
		\item Amplitude, \textbf{A} (Pa).
		\item Frequency, \textbf{f} (Hz): number of cycles per second.
		\item Time period, \textbf{T} (s): the time for one cycle.
		\item Wavelength, $\mathbf{\lambda}$ (m): the distance taken up by one cycle.
		\item Speed \textbf{c} (m/s): the speed at which the wave travels.
	\end{itemize}
\end{frame}

\begin{frame}
	\frametitle{A waveform versus time}
	\setlength{\parskip}{0.5cm}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/100HzVsTime.eps}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{A waveform versus distance}
	\setlength{\parskip}{0.5cm}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/100HzVsDistance.eps}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{The relationship between time and space}
	\vspace{-0.75cm}
	\begin{center}
		\begin{equation*}
		\mathbf {TIME = \frac{1}{FREQUENCY}  \: \: \: \: \: \: \: \: \: \: \Longrightarrow } \: \: \: \: \mathbf {T = \frac{1}{f}}	
		\end{equation*}
		
		\vspace{-0.25cm}
		
		\begin{equation*}
		\mathbf {WAVELENGTH \times FREQUENCY = SPEED  \: \: \: \:  \Longrightarrow}  \: \: \: \: \mathbf {\lambda \times f = c}
		\end{equation*}
		
		\vspace{-0.25cm}
			
		\begin{equation*}
		\mathbf {DISTANCE = SPEED\times TIME  \: \: \: \:  \Longrightarrow}  \: \: \: \: \mathbf {d = c \times t}
		\end{equation*}	
			
		\vspace{0.5cm}
		
		(The speed of sound in air (\textbf{c}) is 343 m/s)
		
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Complex waveforms}
	\begin{itemize}\itemsep16pt
		\item Real musical sounds are more complex than the sine waves shown so far.
		\item But...we can think of a complex waveform as a summation of many different sine waves of different amplitude, frequency (and phase).
	\end{itemize}
\end{frame}


\begin{frame}
	\frametitle{Complex waveforms}
	\vspace{0.5cm}
	This complex waveform...
	\vspace{-0.2cm}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/SummedWave.eps}
	\end{center}
	
\end{frame}

\begin{frame}
	\frametitle{Complex waveforms}
	\vspace{0.5cm}
	...is made by summing these six simple waveforems.
	\vspace{-0.2cm}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/IndividualWaves.eps}
	\end{center}
	
\end{frame}

\begin{frame}
	\frametitle{Sound Features}
	\begin{itemize}\itemsep10pt
		\item There are many different features that we can use to describe a sound.
		\item Today we will consider two types of sound feature:
		\vspace{0.25cm}
		\begin{itemize}\itemsep8pt
			\item Level features.
			\item Spectral features.
		\end{itemize}
	\end{itemize}
\end{frame}

\begin{frame}
	\frametitle{Level Features}
	\vspace{0.2cm}
	There are two key level features: {\bf RMS} and {\bf Peak} level.
	\vspace{-0.2cm}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/RMSandPeak.eps}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Level Features: dynamics}
	\setlength{\parskip}{0.5cm}
	\begin{itemize}\itemsep10pt
			\item The term {\bf dynamics} is used to describe how much a sound varies over time.
	\setlength{\parskip}{0.25cm}
		\begin{itemize}\itemsep6pt
			\item \textbf{Transient sounds} - large fluctuations in amplitude, e.g. percussion.
			\item \textbf{Steady-state sounds} - minimal fluctuations in amplitude, e.g. constant sine-wave.
		\end{itemize}
		\item The {\bf dynamics} are quantified using the {\bf Crest Factor}, which is the logarithmic ratio of {\bf Peak} and {\bf RMS} levels:		
	\end{itemize}
	\begin{equation}
		\mathbf{Crest \ \ Factor} = 20\log_{10}\left(\frac{\mathbf{Peak}}{\mathbf{RMS}}\right)
	\end{equation}		
\end{frame}

\begin{frame}
	\frametitle{Level Features: dynamics}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/CF_SineWave.eps}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Level Features: dynamics}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/CF_Piano.eps}
	\end{center}
\end{frame}
	
\begin{frame}
	\frametitle{Level Features: dynamics}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/CF_Drum.eps}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Level Features: dynamics}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/CF_Clarinet.eps}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Level Features: dynamics}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/CF_Voice.eps}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Level Features: dynamics}
	\setlength{\parskip}{0.5cm}
	\begin{itemize}\itemsep10pt
		\item The {\bf dynamics} are quantified using the {\bf Crest Factor}, which is the logarithmic ratio of {\bf Peak} and {\bf RMS} levels:		
	\begin{equation}
		\mathbf{Crest \ \ Factor} = 20\log_{10}\left(\frac{\mathbf{Peak}}{\mathbf{RMS}}\right)
	\end{equation}		
		\item High Crest Factor $\rightarrow$ Transient.
		\item Low Crest Factor $\rightarrow$ Steady-state.
	\end{itemize}
\end{frame}


\begin{frame}
	\frametitle{Spectral Features}
	\vspace{0.2cm}
	The frequency spectrum of a sound tell us how the energy within the sound is divided into different frequencies.
	\vspace{-0.15cm}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/Spectrum.eps}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Spectral Features}
	\vspace{0.2cm}
	The spikes on the spectrum relate to the individual sine waves from which the sound was composed:	
	\vspace{-0.2cm}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/FrequencyMulti.eps}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Spectral Features}
	\vspace{0.2cm}
	The spikes on the spectrum relate to the individual sine waves from which the sound was composed:	
	\vspace{-0.2cm}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/FrequencyMultiP1.eps}
	\end{center}
\end{frame}
\begin{frame}
	\frametitle{Spectral Features}
	\vspace{0.2cm}
	The spikes on the spectrum relate to the individual sine waves from which the sound was composed:	
	\vspace{-0.2cm}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/FrequencyMultiP2.eps}
	\end{center}
\end{frame}
\begin{frame}
	\frametitle{Spectral Features}
	\vspace{0.2cm}
	The spikes on the spectrum relate to the individual sine waves from which the sound was composed:	
	\vspace{-0.2cm}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/FrequencyMultiP3.eps}
	\end{center}
\end{frame}
\begin{frame}
	\frametitle{Spectral Features}
	\vspace{0.2cm}
	The spikes on the spectrum relate to the individual sine waves from which the sound was composed:	
	\vspace{-0.2cm}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/FrequencyMultiP4.eps}
	\end{center}
\end{frame}
\begin{frame}
	\frametitle{Spectral Features}
	\vspace{0.2cm}
	The spikes on the spectrum relate to the individual sine waves from which the sound was composed:	
	\vspace{-0.2cm}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/FrequencyMultiP5.eps}
	\end{center}
\end{frame}
\begin{frame}
	\frametitle{Spectral Features}
	\vspace{0.2cm}
	The spikes on the spectrum relate to the individual sine waves from which the sound was composed:	
	\vspace{-0.2cm}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/FrequencyMultiP6.eps}
	\end{center}
\end{frame}

\separator{Music Production}

\begin{frame}
	\frametitle{Music Production}
	\begin{center}
		\includegraphics[width = \textwidth]{Figures/mixingCartoon.pdf}
	\end{center}
\end{frame}
		

\separator{Wave Phase}

\begin{frame}
	\frametitle{Wave phase}
 	\begin{itemize}
		\item The position within a cycle of a wave is called the phase and it is defined as a fraction of the wavelength.
	\end{itemize}
	\begin{center}
		\includegraphics[width = 0.85  \textwidth]{Figures/phasefigure.pdf}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Wave phase}
 	\begin{itemize}
		\item The positions are repeated at subsequent cycles of the wave.
	\end{itemize}
	\begin{center}
		\includegraphics[width = 0.85  \textwidth]{Figures/phasefigure2.pdf}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Wave phase}
	\begin{itemize}
		\item The wave phase can be represented on a circle, as an angle.
	\end{itemize}
	\begin{center}
		\includegraphics[height = 0.8 \textheight]{Figures/phaseAngle.pdf}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Wave phase}
 	\begin{itemize}\itemsep24pt
		\item Why do we care about wave phase as audio people?
		\item We care, because the \textbf{difference} in phase is critical when we are adding waves together, and this is something we do \textbf{A LOT} in audio!	
		\item Adding waves: 1 + 1 = ...?
	\end{itemize}

\end{frame}

\begin{frame}
	\frametitle{Adding waves - in phase}
% 	\begin{itemize}
%		\item Adding waves which are in phase (no difference in phase).
%	\end{itemize}
	\begin{center}
	\includegraphics[width = 0.85  \textwidth]{Figures/phaseadd1.pdf}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Adding waves - 1/8 cycle}
% 	\begin{itemize}
%		\item Adding waves with a phase difference of $\frac{1}{8}\lambda$.
%	\end{itemize}
	\begin{center}
	\includegraphics[width = 0.85  \textwidth]{Figures/phaseadd2.pdf}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Adding waves - 1/4 cycle}
% 	\begin{itemize}
%		\item Adding waves with a phase difference of $\frac{1}{4}\lambda$.
%	\end{itemize}
	\begin{center}
	\includegraphics[width = 0.85  \textwidth]{Figures/phaseadd3.pdf}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Adding waves - 3/8 cycle}
% 	\begin{itemize}
%		\item Adding waves with a phase difference of $\frac{3}{8}\lambda$.
%	\end{itemize}
	\begin{center}
	\includegraphics[width = 0.85  \textwidth]{Figures/phaseadd4.pdf}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Adding waves - out of phase}
% 	\begin{itemize}
%		\item Adding waves with a phase difference of $\frac{1}{2}\lambda$ (completely out of phase).
%	\end{itemize}
	\begin{center}
	\includegraphics[width = 0.85  \textwidth]{Figures/phaseadd5.pdf}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Adding waves - 5/8 cycle}
% 	\begin{itemize}
%		\item Adding waves with a phase difference of $\frac{5}{8}\lambda$.
%	\end{itemize}
	\begin{center}
	\includegraphics[width = 0.85  \textwidth]{Figures/phaseadd6.pdf}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Adding waves - 3/4 cycle}
% 	\begin{itemize}
%		\item Adding waves with a phase difference of $\frac{3}{4}\lambda$.
%	\end{itemize}
	\begin{center}
	\includegraphics[width = 0.85  \textwidth]{Figures/phaseadd7.pdf}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Adding waves - 7/8 cycle}
% 	\begin{itemize}
%		\item Adding waves with a phase difference of $\frac{7}{8}\lambda$.
%	\end{itemize}
	\begin{center}
	\includegraphics[width = 0.85  \textwidth]{Figures/phaseadd8.pdf}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Adding waves - back in phase}
% 	\begin{itemize}
%		\item Adding waves with a phase difference of $\lambda$ (back in phase).
%	\end{itemize}
	\begin{center}
	\includegraphics[width = 0.85  \textwidth]{Figures/phaseadd9.pdf}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Adding waves}
	\begin{center}
		\includegraphics[width = 0.85  \textwidth]{Figures/phaseAngleOnePlusOne.pdf}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Adding waves}
	\begin{center}
		\includegraphics[width = 0.85  \textwidth]{Figures/phaseAngleOnePlusOne-180.pdf}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Inverting Phase}
	\vspace{0.5cm}
	Phase is inverted when we `flip' the signal across the time axis.	
	\vspace{-0.2cm}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/WaveInPhase.eps}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Inverting Phase}
	\vspace{0.5cm}
	Phase is inverted when we `flip'  the signal across the time axis.
	\vspace{-0.2cm}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/WavePhaseInvert.eps}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Inverting Phase}
	\vspace{0.3cm}
	Adding inverted and non-inverted signals causes cancellation!
	\vspace{-0.2cm}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/InvertCancellation.eps}
	\end{center}
\end{frame}


\begin{frame}
	\frametitle{Phase change with frequency}
	\begin{itemize}\itemsep16pt
		\item Phase differences between two sounds can vary as a function of frequency.
		\item You cannot hear the difference in phase when the signal is played in isolation, but you will hear it when two signals are added together!
	\end{itemize}
\end{frame}

\begin{frame}
	\frametitle{Phase change with frequency}
	\vspace{0.5cm}
	Sound A:
	\vspace{-0.2cm}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/SoundA.eps}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Phase change with frequency}
	\vspace{0.5cm}
	Sound B:
	\vspace{-0.2cm}
	\begin{center}
		\includegraphics[width =  \textwidth]{Figures/SoundB.eps}
	\end{center}
\end{frame}

\begin{frame}
	\frametitle{Phase changes due to time delay}
	\begin{itemize}\itemsep16pt
		\item If two sounds are added with a time offset there will be a frequency dependent phase difference.
		\item A time delay of $\mathbf{\tau}$ ms is added and can be expressed as a percentage of the time period, $\mathbf{T}$, to give a phase shift.
		\begin{equation*}
			 \theta = \frac{\tau} {\mathbf{T}} \ \ \times \ \ 360 .
		\end{equation*}
	\end{itemize}
\end{frame}

\begin{frame}
	\frametitle{Phase changes due to time delay}
	\begin{itemize}\itemsep10pt
		\item What happens if we add a delayed copy of Sound A to the original?
		\item Sound A has frequency components: $\mathbf{F_1} = 100$ Hz, $\mathbf{F_2}=500$ Hz and $\mathbf{F_3}=8000$ Hz.
		\item These relate to time periods: $\mathbf{T_1} = 10$ ms, $\mathbf{T_2}=2$ ms Hz and $\mathbf{T_3}=0.125$ ms.
		\end{itemize}
\end{frame}

\begin{frame}
	\frametitle{Phase changes due to time delay}
	\begin{itemize}\itemsep10pt
		\item If $\tau=1$ ms:
		\begin{eqnarray}
			\theta_1 = \frac{1}{10} \times 360 = 36^o. \\			
			\theta_2 = \frac{1}{2} \times 360 = 180^o. \\
			\theta_3 = \frac{1}{0.125} \times 360 = 2880^o = 0^o.
		\end{eqnarray}
			
	\end{itemize}
\end{frame}
		
\begin{frame}
	\frametitle{Phase changes due to time delay}
	\vspace{0.5cm}
	The effect of $\tau = 1$ ms plotted against frequency: referred to as a comb filter.
	\vspace{-0.2cm}
	\begin{center}
		\includegraphics[width = 0.95  \textwidth]{Figures/CombFilter.eps}
	\end{center}
\end{frame}



\end{document}