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slit interference</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../1124/thin-film-interference.html">Thin film interference</a></label></li></ul></li></ul></div> <div class="hidden-xs hidden-sm"> <button class="btn btn-default btn-block text-xs-center" data-toggle="modal" data-target="#modal-feedback" style="margin-bottom: 10px"><i class="fa fa-send"></i> Feedback</button> </div> </div> <div class="col-md-9" id="main-column"> <h1 class="page_title"> Phase <a href="#" class="mark-page-favorite pull-right" data-pid="277" title="Mark as favorite" onclick="return false;"><i class="fa fa-star-o"></i></a> </h1> <ol class="breadcrumb"> <li><a href="../../../physics.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../444/oscillations-and-waves.html">Oscillations and waves</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../272/oscillations.html">Oscillations</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Phase</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 10 minutes"><i class="fa fa-clock-o"></i> 10'</span> </ol> <article id="main-article"> <p><img alt="" src="../../waves/3-juggler-sm.jpg" style="float: left; width: 250px; height: 170px;">A juggler may not understand the mathematical representation of phase, but they are using the effect as they throw balls in the air at different times.</p> <p>It is important to understand the concept of phase before starting the <a href="../278/waves.html" title="Waves">Waves</a> section. In short: a full wave cycle consists of 2<em>π </em>radians.</p> <hr class="hidden-separator"> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <div> <p>The oscillations of two pendula can be represented by two sine or cosine curves. If the pendulums don't swing at the same time, the curves will not be together and instead will be separated by an angle <em>φ</em>. This is called the phase difference or phase angle.</p> <p>A phase angle of <em>π</em> means that the pendula are completely out of phase (antiphase), whereas phase angles of 0 or 2<em>π </em>make the pendula oscillate in phase.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/168004318"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div> <div class="panel panel-yellow panel-has-colored-body panel-has-border"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Pendulum pattern</p> </div> </div> <div class="panel-body"> <div> <p>Pendula in a line, each swinging at a slightly different frequency, will go in and out of phase with one another.</p> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/168005645"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-yellow panel-has-colored-body panel-has-border panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Rotating vectors </p> </div> </div> <div class="panel-body"> <div> <p>A little bit extra for those who are interested: phase difference can be represented with <em>rotating vectors</em>.</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/179004951"></iframe></div> </section> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test Yourself</p> </div> </div> <div class="panel-body"> <div> <p><i>Use quizzes to practise application of theory.</i></p> <br><a class="btn btn-primary btn-block text-center" data-toggle="modal" href="#dfb920fa"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="dfb920fa"> <div class="modal-dialog" style="width: 95vw; max-width: 960px"> <div class="modal-content"> <div class="modal-header slide-quiz-title"> <h4 class="modal-title" style="width: 100%;"> Phase <strong class="q-number pull-right"> <span class="counter">1</span>/<span class="total">1</span> </strong> </h4> </div> <div class="modal-body p-xs-3"> <div class="slide-quiz" data-stats="6-85-277" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>The two lines on the graph below represent two oscillating bodies.</p><p style="text-align: center;"><img alt="" src="../../phaseq1.jpg" style="width: 372px; height: 156px;"></p><p>The phase difference between the bodies is:</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> π</label></p><p><label class="radio"><input type="radio"> π/4</label></p><p><label class="radio"><input class="c" type="radio"> π/2</label></p><p><label class="radio"><input type="radio"> 2π</label></p></div><div class="q-explanation"><p>The oscillations are 1/4 of a cycle out of phase. 1 cycle is 2π</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The two lines on the graph below represent two oscillating bodies.</p><p style="text-align: center;"><img alt="" src="../../phaseq2.jpg" style="width: 372px; height: 156px;"></p><p>The phase difference between the bodies is:</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> π/2</label></p><p><label class="radio"><input type="radio"> 2π</label></p><p><label class="radio"><input class="c" type="radio"> π</label></p><p><label class="radio"><input type="radio"> π/4</label></p></div><div class="q-explanation"><p>The oscillations are 1/2 of a cycle out of phase. 1 cycle is 2π</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The two lines on the graph represent two oscillating bodies:</p><p style="text-align: center;"><img alt="" src="../../phaseq3.jpg" style="width: 372px; height: 156px;"></p><p>The ratio of frequency of red/frequency of blue is</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 3/4</label></p><p><label class="radio"><input class="c" type="radio"> 2/3</label></p><p><label class="radio"><input type="radio"> 4/3</label></p><p><label class="radio"><input type="radio"> 3/2</label></p></div><div class="q-explanation"><p>Between the two points where the oscillations are in phase there are 2 red cycles and 3 blue cycles. So ratio of time periods is 3/2. Frequency = 1/T so ratio of frequencies =2/3</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The animation is of 2 bodies executing SHM</p><p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="/media/physics/phasq5.gif" style="width: 163px; height: 148px;"></p></div><div class="q-answer"><p><label class="radio"><input type="radio"> B leads A by π</label></p><p><label class="radio"><input class="c" type="radio"> B leads A by π/2</label></p><p><label class="radio"><input type="radio"> A leads B by π/2</label></p><p><label class="radio"><input type="radio"> A leads B by π</label></p></div><div class="q-explanation"><p>1/4 cycle out of phase, when Ais in the middle B is at the top</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The animation is of 2 bodies executing SHM</p><p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="/media/physics/phaseq6.gif" style="width: 163px; height: 148px;"></p><p>The phase difference is</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> π/2</label></p><p><label class="radio"><input type="radio"> 2π</label></p><p><label class="radio"><input class="c" type="radio"> π</label></p><p><label class="radio"><input type="radio"> 3π/2</label></p></div><div class="q-explanation"><p>half a cycle</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The displacement of two bodies can be represented by the equations:</p><p style="text-align: center;">y<sub>1</sub> = Asin(2πft + π)</p><p style="text-align: center;">y<sub>2</sub> = A sin(2πft + π/4)</p><p>The phase difference is</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 5π/4</label></p><p><label class="radio"><input type="radio"> 2π</label></p><p><label class="radio"><input class="c" type="radio"> 3π/4</label></p><p><label class="radio"><input type="radio"> π/4</label></p></div><div class="q-explanation"><p>The phase angle of 1 is π and 2 is π/4. The phase difference is the difference in phase angle</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Tow bodies execute SHM with different frequency.</p><p>If they start in phase they will</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> always be in phase</label></p><p><label class="radio"><input class="c" type="radio"> be in phase again at regular intervals</label></p><p><label class="radio"><input type="radio"> be in phase again at random times</label></p><p><label class="radio"><input type="radio"> never be in phase again</label></p></div><div class="q-explanation"><p>The time between them being in phase depends on the difference in frequency</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The anim,ation shows 2 points oscillating out of phase</p><p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="/media/physics/phaseq7.gif" style="width: 117px; height: 209px;"></p><p>Which phase diagram represent this situation?</p><p style="text-align: center;"><img alt="" height="416" src="../../phaseq7.jpg" width="410"></p></div><div class="q-answer"><p><label class="radio" style=" float: left; margin-right: 40px; "><input class="c" type="radio"> A</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> B</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> C</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> D</label></p></div><div class="q-explanation"><p>Phase difference is less than π/2</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The graphs y = sin θ (red) and y = cos θ (blue) are shown below</p><p style="text-align: center;"><img alt="" height="197" src="../../sincos.jpg" width="299"></p><p>The equation relating the functions is</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> cos θ = sin (θ - π)</label></p><p><label class="radio"><input class="c" type="radio"> cos θ = sin (θ + π/2)</label></p><p><label class="radio"><input type="radio"> cos θ = sin (θ - π/2)</label></p><p><label class="radio"><input type="radio"> cos θ = sin (θ + π)</label></p></div><div class="q-explanation"><p>cos (0) is the same as sin (0 + π/2)</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> 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