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href="../1123/resolution.html">Resolution</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../1126/multiple-slit-interference.html">Multiple 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"> Wave phenomena <a href="#" class="mark-page-favorite pull-right" data-pid="365" 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="../278/waves.html">Waves</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Wave phenomena</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 15 minutes"><i class="fa fa-clock-o"></i> 15'</span> </ol> <article id="main-article"> <p><img alt="" src="../../small-images/screen-shot-2016-11-04-at-05.47.30.png" style="float: left; width: 250px; height: 222px;">On this page we will examine the wave phenomena of reflection, refraction, interference, diffraction and polarisation, as well as the concept of standing (or stationary) waves.</p> <p>To show these in a visual way we will use a ripple tank simulation. Wave simulations use the same mathematical equations that are used to model real waves. Therefore they have have the same properties. </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> <div class="panel panel-turquoise panel-has-colored-body panel-has-border"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Reflection</p> </div> </div> <div class="panel-body"> <div> <p>When a wave hits a boundary or change in medium, it reflects back. Each point on the boundary behaves like a small wavelet source.</p> <p style="text-align: center;">the angle of incidence = the angle of reflection</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/168462896"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-turquoise 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>Refraction</p> </div> </div> <div class="panel-body"> <div> <p>When a wave travels into a more dense medium, it slows down. This causes the wave to change direction.</p> <p style="text-align: center;"><span class="math-tex">\({\sin i\over \sin r}={v_1\over v_2}\)</span></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/168463327"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <p> </p> </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-has-colored-body panel-has-border panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Interference</p> </div> </div> <div class="panel-body"> <div> <p>When two balls collide, they bounce off each other. When two waves collide, they pass through each other.</p> <p>Where the waves overlap the amplitudes add, this is called <em>superposition.</em> This results in interference effects.</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/168464081"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Diffraction</p> </div> </div> <div class="panel-body"> <div> <p>When a wave passes through an opening in a barrier, it spreads out. Diffraction is optimised where the width of the opening is approximately equal in size to the wavelength.</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/168895068"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Polarisation</p> </div> </div> <div class="panel-body"> <div> <p>A wave in a guitar string, like many examples of waves, oscillates in all directions.</p> <p>A polarised wave only oscillates in one direction.</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/168896560"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Standing waves </p> </div> </div> <div class="panel-body"> <div> <p>A standing wave is formed when two waves, of equal frequency and amplitude, travelling in opposite directions interfere.</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/170909316"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <p> </p> </div> </div> <div class="panel-footer"> <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="#be8035a1"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="be8035a1"> <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%;"> Wave properties <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="6-87-365" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>The diagram shows a ray of light reflecting off a mirror</p><p style="text-align: center;"><img alt="" src="../../reflectionq1.jpg" style="width: 238px; height: 148px;"></p><p>The angle of incidence is</p></div><div class="q-answer"><p><label class="radio" style=" float: left; margin-right: 40px; "><input class="c" type="radio"> B</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> A</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>angles are measure to the normal</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 diagram shows a wavefront incident on then reflecting off a boundary.</p><p style="text-align: center;"><img alt="" src="../../reflectionq2.jpg" style="width: 439px; height: 179px;"></p><p>Which angle is the angle of reflection?</p></div><div class="q-answer"><p><label class="radio" style=" float: left; margin-right: 40px; "><input class="c" type="radio"> C</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input 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"> D</label></p></div><div class="q-explanation"><p>The angle of reflection is the angle between the ray and the normal. This is the same as the angle shown</p><p style="text-align: center;"><img alt="" src="../../reflectionans2.jpg" style="width: 221px; height: 221px;"></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>This diagram represents a circular wavefront incident on a plane boundary.</p><p style="text-align: center;"><img alt="" src="../../refelctionq3.jpg" style="width: 492px; height: 234px;"></p><p>Which of the red lines represents the reflected wavefront?</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>The centre of the reflected wave should be the same distance behind the reflector as the centre of the incident wave is in front.</p><p style="text-align: center;"><img alt="" src="../../reflectiona3.jpg" style="width: 397px; height: 348px;"></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 diagram represents a plane wavefront passing from medium 1 to 2 with 4 possible angles of refraction.</p><p style="text-align: center;"><img alt="" src="../../refractioq3.jpg" style="width: 278px; height: 313px;"></p><p>If the wave speed in 2 is greater than 1 the refracted wave could be:</p></div><div class="q-answer"><p><label class="radio" style=" float: left; margin-right: 40px; "><input class="c" type="radio"> B</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> A</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>The wave direction moves towards the normal</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 diagram represents a plane wavefront passing from medium 1 to 2 with 4 possible angles of refraction.</p><p style="text-align: center;"><img alt="" src="../../refractioq3.jpg" style="width: 278px; height: 313px;"></p><p>If the wave speed in 1 is greater than 2 the refracted wave could be:</p></div><div class="q-answer"><p><label class="radio" style=" float: left; margin-right: 40px; "><input class="c" type="radio"> D</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> A</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"> B</label></p></div><div class="q-explanation"><p>The wave direction moves towards the normal</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 diagram shows a wave refracting as it passes from one medium to another.</p><p style="text-align: center;"><img alt="" src="../../refractq4.jpg" style="width: 241px; height: 205px;"></p></div><div class="q-answer"><p>velocity in medium 1/velocity in medium 2 <input type="text" style="height: auto;" data-c="0.53"> <span class="review"></span> (2dp)</p><p style="text-align: center"><iframe height="420" scrolling="no" src="http://web2.0calc.com/widgets/horizontal/?options=%7B%22angular%22%3A%22deg%22%2C%22options%22%3A%22hide%22%2C%22menu%22%3A%22show%22%7D" style="border: 1px solid silver; " width="590"></iframe><br><a href="http://web2.0calc.com/">Web 2.0 scientific calculator</a></p></div><div class="q-explanation"><p>v<sub>1</sub>/v<sub>2</sub> = sin i<sub>1</sub>/sin i<sub>2 </sub>= sin 30°/sin70°</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>A plane wave passes across the boundary from one medium to another as shown.</p><p style="text-align: center;"><img alt="" src="../../refractq5.jpg" style="width: 204px; height: 164px;"></p><p>The ratio velocity in medium 1/velocity in medium 2 is</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 1</label></p><p><label class="radio"><input class="c" type="radio"> 2</label></p><p><label class="radio"><input type="radio"> 0.25</label></p><p><label class="radio"><input type="radio"> 0.5</label></p></div><div class="q-explanation"><p>Since frequency is the same in both media v is proportional to λ (v = fλ)</p><p>v<sub>1</sub>/v<sub>2</sub> = λ<sub>1</sub>/λ<sub>2</sub> = 2/1</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>This is a screenshot from Paul Falstad´s ripple tank simuator</p><p style="text-align: center;"><img alt="" height="208" src="../../screen-shot-2016-08-20-at-08.31.56.png" width="281"></p><p>In the blue area the water is</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> warmer</label></p><p><label class="radio"><input type="radio"> deeper</label></p><p><label class="radio"><input type="radio"> colder</label></p><p><label class="radio"><input class="c" type="radio"> shallower</label></p></div><div class="q-explanation"><p>The wave travels slower in the blue area so the water is less deep.</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>This image is a screenshot from Paul Falstad´s ripple tank simulator</p><p style="text-align: center;"><img alt="" src="../../interferq1.jpg" style="width: 183px; height: 183px;"></p><p>If the difference between distance XP and YP is 2 cm the wavelength is:</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 1 cm</label></p><p><label class="radio"><input type="radio"> 0.5 cm</label></p><p><label class="radio"><input class="c" type="radio"> 4 cm</label></p><p><label class="radio"><input type="radio"> 2cm</label></p></div><div class="q-explanation"><p>P is in the first minimum so path difference = λ/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>This image is a screenshot from Paul Falstad´s ripple tank simulator</p><p style="text-align: center;"><img alt="" src="../../interferq2.jpg" style="width: 183px; height: 183px;"></p><p>If the difference between distance XP and YP is 2 cm the wavelength is:</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> 2 cm</label></p><p><label class="radio"><input type="radio"> 0.5 cm</label></p><p><label class="radio"><input type="radio"> 1 cm</label></p><p><label class="radio"><input type="radio"> 4cm</label></p></div><div class="q-explanation"><p>P is in the first maximum so path difference = λ</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>This screenshot from Paul Falstad´s ripple tank shows waves diffracting through a single slit</p><p style="text-align: center;"><img alt="" height="203" src="../../diffq1.png" width="293"></p><p>The waves would definitely spread out more if:</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> the slit width is reduced and the wavelength reduced</label></p><p><label class="radio"><input type="radio"> the slit width is increased and the wavelength reduced</label></p><p><label class="radio"><input type="radio"> the slit width is increased and the wavelength increased</label></p><p><label class="radio"><input class="c" type="radio"> the slit width is reduced and the wavelength increased</label></p></div><div class="q-explanation"><p>reducing the slit width and increasing wavelength both result in a wider 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>This screenshot from Paul Falstad´s ripple tank shows waves diffracting through a single slit</p><p style="text-align: center;"><img alt="" src="../../diffq2.jpg" style="width: 243px; height: 241px;"></p><p>If the slit width is reduced:</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> the angle decreases and the amplitude gets more</label></p><p><label class="radio"><input class="c" type="radio"> The angle increases and the amplitude gets less</label></p><p><label class="radio"><input type="radio"> the angle decreases and the amplitude stays the same</label></p><p><label class="radio"><input type="radio"> the angle increases and the amplitude stays the same</label></p></div><div class="q-explanation"><p>angle of diffraction increases and less wave passes through the slit so the amplitude is reduced</p><p style="text-align: center;"><img alt="" height="162" src="../../screen-shot-2016-08-20-at-10.51.34.png" width="231"></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 diagram below shows a wave in a string incident on a narrow slit.</p><p style="text-align: center;"><img alt="" src="../../polarq1.jpg" style="width: 256px; height: 179px;"></p><p>When the wave passes though the slit it will:</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> have zero amplitude</label></p><p><label class="radio"><input type="radio"> have a smaller amplitude and oscillate vertically</label></p><p><label class="radio"><input class="c" type="radio"> have a smaller amplitude and oscillate in the plane of the slit</label></p><p><label class="radio"><input type="radio"> have the same amplitude but oscillate in the plane of the slit</label></p></div><div class="q-explanation"><p>Only the component in the direction of the slit will pass through.</p><p style="text-align: center;"><img alt="" height="130" src="../../screen-shot-2016-08-20-at-13.38.04.png" width="176"></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>An unpolarised wave passes along a string. When it meets a vertical slit</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> the vertical component of all oscillations will pass</label></p><p><label class="radio"><input type="radio"> oscillations perpendicular to the slit will pass</label></p><p><label class="radio"><input type="radio"> no oscillations pass</label></p><p><label class="radio"><input type="radio"> only vertical oscillations pass</label></p></div><div class="q-explanation"><p>I´m not sure what would actually happen but according to this simple model all components in line with the slit will pass.</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>When a guitar string is plucked, the wave</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> is polarised but only when high notes are played</label></p><p><label class="radio"><input type="radio"> can not be polarised</label></p><p><label class="radio"><input type="radio"> is polarised</label></p><p><label class="radio"><input class="c" type="radio"> isn´t polarised but it can be if the string is restricted</label></p></div><div class="q-explanation"><p>The wave isn´t normally polarised but can be if you restrict it lightly with your finger.</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>A standing wave is formed when the wave shown reflects off the fixed end.</p><p style="text-align: center;"><img alt="" src="../../standwaveq1.jpg" style="width: 333px; height: 146px;"></p><p>The distance between nodes will be:</p></div><div class="q-answer"><p><label class="radio"><input class="c" type="radio"> 1 m</label></p><p><label class="radio"><input type="radio"> 2 m</label></p><p><label class="radio"><input type="radio"> 0.5 m</label></p><p><label class="radio"><input type="radio"> 4 m</label></p></div><div class="q-explanation"><p style="text-align: center;"><img alt="" src="../../standwavea1.jpg" style="width: 248px; height: 169px;"></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>A standing wave can be formed in a string by vibrating each end. This causes waves to travel along the string in both directions, these waves add to give a standing wave.</p><p>To form a standing wave the sources do <strong>not </strong>have to be</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> the same amplitude</label></p><p><label class="radio"><input type="radio"> the same frequency</label></p><p><label class="radio"><input type="radio"> on opposite ends of the string</label></p><p><label class="radio"><input class="c" type="radio"> in phase</label></p></div><div class="q-explanation"><p>changing the phase wil change the positions of the nodes but a standing wave can still be formed. 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