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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"> Waves <a href="#" class="mark-page-favorite pull-right" data-pid="278" 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><span class="gray">Waves</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 30 minutes"><i class="fa fa-clock-o"></i> 30'</span> </ol> <article id="main-article"> <p><img alt="" src="../../waves/disperse-1.jpg" style="float: left; width: 250px; height: 166px;">A wave is a transfer of energy or information using oscillations of a medium, without moving the particles of the medium themselves.</p> <p>Waves can be modelled mathematically and have a number of different 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-has-colored-body panel-has-border panel-turquoise"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Wave phenomena</p> </div> </div> <div class="panel-body"> <div> <p>All waves have the following chracteristics:</p> <hr class="hidden"> <p><strong>Reflection: </strong>When a wave hits a barrier it comes back. The angle of reflection is equal to the angle of incidence.</p> <hr class="hidden"> <p><strong>Refraction: </strong>When a wave passes into another medium, it changes direction due to a change in speed.</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p style="text-align: center;"><img alt="" src="../../../ib/physics/activities/refraction1.png" style="width: 346px; height: 267px;"></p> <p style="text-align: center;"><img align="middle" alt="fraction numerator sin i over denominator sin r end fraction equals v subscript 1 over v subscript 2" class="Wirisformula" data-mathml="«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»sin«/mi»«mi»i«/mi»«/mrow»«mrow»«mi»sin«/mi»«mi»r«/mi»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«msub»«mi»v«/mi»«mn»1«/mn»«/msub»«msub»«mi»v«/mi»«mn»2«/mn»«/msub»«/mfrac»«/math»" src="../../../ckeditor/plugins/wiris/integration/showimage-44.php?formula=339ff1735798bae26e94940bc4b3d0ac.png"></p> </section> <hr class="hidden"> <p><strong>Interference: </strong>When two waves of the same type meet, they combine to construct and destruct one another.</p> <p><strong>Superposition: </strong>The total displacement of interfering waves is the vector sum of the individual displacements.</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p style="text-align: center;"><img alt="" src="../../../ib/physics/activities/falstadinterference.png" style="width: 311px; height: 254px;"></p> <p>Waves add at point P since the path difference is one whole wavelength. Waves cancel at Q since the path difference is half a wavelength.</p> </section> <hr class="hidden"> <p><strong>Diffraction: </strong>When a wave passes through a narrow opening it spreads out. A wave will also pass around the edge of a barrier.</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="https://teacher-sites-storage-test.s3.eu-west-1.amazonaws.com/ib/physics/activities/difsound.gif"></p> <p>In this animation you can see how the wavelets making up a wave front passing through a small opening spread out forming areas of constructive and destructive interference.</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="https://teacher-sites-storage-test.s3.eu-west-1.amazonaws.com/ib/physics/falstaddiff.gif"></p> </section> <p><img class="sibico" src="../../../img/sibico/exam-style.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="Exam-style question"> The Huygens construction explains the properties of a wave by considering the wave front (e.g. a peak or a compression) to be made of an infinite number of small wavelet sources. Each wavelet progresses forwards, adding to give the new wave front. </p> </section> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-turquoise panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Wave quantities</p> </div> </div> <div class="panel-body"> <div> <p style="text-align: center;"><u><img alt="" src="../../../ib/physics/activities/wavequants.png" style="width: 469px; height: 143px;"></u></p> <p>You will need to memorise the following definitions:</p> <p><strong>Amplitude (<em>A</em>): </strong>The maximum displacement from the equilibrium position.</p> <p><strong>Wave speed (<em>v</em>): </strong>The distance moved by the wave per second.</p> <p><strong>Wavelength (<em>λ</em>): </strong>The distance between two equivalent points on consecutive waves (e.g. peak to peak)</p> <p><strong>Frequency (<em>f</em>): </strong>The number of complete cycles passing a point per second or the number of waves produced every second.</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-turquoise panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Wave types</p> </div> </div> <div class="panel-body"> <div> <p>In a <strong>transverse </strong>wave, the direction of displacement is perpendicular to the direction of propagation. Examples include:</p> <ul> <li>water waves</li> <li>waves on a string</li> <li>electromagnetic waves</li> <li>S-earthquake waves</li> </ul> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="https://teacher-sites-storage-test.s3.eu-west-1.amazonaws.com/ib/physics/activities/transverse.gif" style="width: 440px; height: 148px;"></p> </section> <p>Transverse waves have peaks and troughs. </p> <p>A wave is said to be polarised if the displacement is restricted to one plane. This plane could be vertical, horizontal or anything in between. If a wave can be polarised, it must be transverse.</p> <p>In a <strong>longitudinal</strong> wave, the direction of displacement is parallel to the direction of propagation. Examples include:</p> <ul> <li>sound waves</li> <li>compression waves on a slinky spring</li> <li>P-earthquake waves</li> </ul> <p>NB: Where possible, avoid using 'slinky spring' as an example of a transverse or longitudinal wave, as you will not be giving an unambigous response.</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="https://teacher-sites-storage-test.s3.eu-west-1.amazonaws.com/ib/physics/activities/longwave.gif" style="width: 440px; height: 148px;"></p> </section> <p>There are no peaks and troughs in a longitudinal wave, instead there are compressions and rarefactions.</p> <h4 style="text-align: center;"><img alt="" src="../../../ib/physics/longrare.png" style="width: 607px; height: 179px;"></h4> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-turquoise panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Graphical representation of progressive waves</p> </div> </div> <div class="panel-body"> <div> <p><strong>Displacement vs position</strong></p> <p style="text-align: center;"><img alt="" src="../../../ib/physics/activities/lpwavean1.png" style="width: 544px; height: 279px;"></p> <p><strong>Displacement vs time</strong></p> <p style="text-align: center;"><img alt="" src="../../../ib/physics/activities/lpwavean2.png" style="width: 556px; height: 286px;"></p> <p>The displacement time graph for a <strong>longitudinal wave</strong> is plotted in the same way as for a transverse wave, but the displacement position is a bit more tricky since the displacement is parallel to the wave direction.</p> <p style="text-align: center;"><img alt="" src="../../images/longgraph.png" style="width: 600px; height: 267px;"></p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-turquoise panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Wave equations</p> </div> </div> <div class="panel-body"> <div> <p>We recall from <a href="../218/kinematics.html" title="Kinematics">Kinematics</a> that speed is distance divided by time. Given that all individual waves travel at the same speed in a given medium, it is often more convenient to consider calculating the speed of just one wave:</p> <div class="box"> <p style="text-align: center;"><span class="math-tex">\(v={\lambda \over T}\)</span></p> <p style="text-align: center;">Since <span class="math-tex">\(T={1\over f}\)</span>, <span class="math-tex">\(v=f\lambda\)</span></p> </div> <p>NB: A stretched string has a wave speed related to the tension in the string and the mass per unit length of the string:<img align="middle" alt="v space equals space square root of T over mu end root" class="Wirisformula" data-mathml="«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»v«/mi»«mo»§#x000A0;«/mo»«mo»=«/mo»«mo»§#x000A0;«/mo»«msqrt»«mfrac»«mi»T«/mi»«mi»§#x003BC;«/mi»«/mfrac»«/msqrt»«/math»" src="../../../ckeditor/plugins/wiris/integration/showimage-45.php?formula=e31f60342515340012341f8698e9a919.png"></p> <p><em>T</em> (N) = tension<br> <em>μ</em> (kg m<sup>-1</sup>) = mass per unit length</p> <p><img class="sibico" src="../../../img/sibico/hl-red.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="HL difficult"> It is possible to find an equation for how the <em>y</em>-displacement of a wave varies with the distance travelled (<em>x</em>) through the medium: <span class="math-tex">\(y=A\sin(2\pi ft-{2\pi \over \lambda}x)\)</span></p> <h4>Standing waves</h4> <p>Standing waves (or stationary waves) form when the following occurs:</p> <ul> <li>Two waves</li> <li>With the same freqency and amplitude</li> <li>Travelling in opposite directions</li> <li>Interfere with each other</li> </ul> <p>The most regular occurence of this is a single wave reflecting back onto itself.</p> <p>Standing waves are represented by drawing the two extremes in position.</p> <p style="text-align: center;"><img alt="" src="../../../ib/physics/activities/harmonics.png" style="width: 312px; height: 307px;"></p> <p><strong>Node:</strong> Point that has zero amplitude</p> <p><strong>Antinode: </strong>Point with maximum amplitude</p> <p>All sections between two nodes oscillate perfectly in phase.</p> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </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-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>Sound</p> </div> </div> <div class="panel-body"> <div> <p>When air is disturbed it causes a change in pressure. This in turn disturbs the surrounding air, resulting in propagation of changing pressure throughout the medium.</p> <p>Sound waves can be simulated using Algodoo.</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="https://teacher-sites-storage-test.s3.eu-west-1.amazonaws.com/ib/physics/activities/sound1.gif"></p> </section> <div class="doNotShow hiddenContent" id="hiddenBoxContent1">Sound is not just something to be measured; it can also be experienced with our senses. The <em>loudness</em> and <em>pitch</em> of a sound are related to the physical quantities of amplitude and frequency, respectively.</div> <div class="doNotShow hiddenContent"> <div class="box"> <p style="text-align: center;">High pitch = high frequency<br> Loud sound = large amplitude<br> Speed = 340 ms<sup>-1</sup></p> </div> </div> <p>Sound changes speed when it enters a new material (the denser the material, the more particles present, and the faster the propagation of pressure. In fact, sound will not travel through a vacuum.</p> <p>Sound is also refracted as it passes through air of a different temperature.</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p style="text-align: center;"><img alt="" class="gifffer" data-gifffer="https://teacher-sites-storage-test.s3.eu-west-1.amazonaws.com/ib/physics/activities/soundrefract.gif"></p> </section> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-expandable panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Light</p> </div> </div> <div class="panel-body"> <div> <p>The properties of electromagnetic waves depend on their wavelength. Radio waves have the longest wavelength and gamma waves the shortest. Conversely (due to the constant speed of light, <span class="math-tex">\(c=3\times10^8\)</span>ms<sup>-1</sup>), radio waves have the lowest frequency and gamma waves the highest. </p> <p>We can display all the different wavelengths on a chart; this is called a spectrum.</p> <p style="text-align: center;"><img alt="" src="../../../ib/physics/activities/emspectrum.png" style="width: 593px; height: 97px;"></p> <p style="text-align: center;"><img alt="" src="../../../ib/physics/activities/visible.png" style="width: 393px; height: 108px;"></p> <p>We can produce a spectrum of visible white light by separating the wavelengths using a prism. Red light maintains its speed best in glass and so refracts least, whereas violet light reduces in speed the most and refracts most.</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p style="text-align: center;"><img alt="" src="../../../ib/physics/activities/prismbr.png" style="width: 418px; height: 215px;"></p> </section> <p>As with sound waves, humans are able to sense visible light:</p> <p style="text-align: center;">Wavelength → colour<br> Amplitude → brightness</p> <p><strong>Brightness:</strong> directly related to the <em>intensity</em> (power per unit area), brightness is proportional to the square of the amplitude.</p> <p><strong>Reflection: </strong>the reason we see objects is because they reflect light into our eyes. When light reflects, the angle of reflection equals the angle of incidence. However, this is only noticeable when the surface is smooth.</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p style="text-align: center;"><img alt="" src="../../../ib/physics/activities/redifrefl.png" style="width: 577px; height: 129px;"></p> </section> <p><strong>Refraction: </strong>When light passes from one medium to another its velocity changes resulting in a change of direction.</p> <p style="text-align: center;"><img alt="" src="../../../ib/physics/activities/iandr.png" style="width: 196px; height: 161px;"></p> <div class="box"> <p>A mathematical relationship can be used to calculate the angle of refraction in the new material. It depends on the refractive indices (plural: index) of the materials:</p> <p style="text-align: center;"><span class="math-tex">\(n_1 \sin i_1=n_2 \sin i_2\)</span></p> <p>Refractive index is defined of the ratio of the speed of light in a vacuum to the speed of light in the material:</p> <p style="text-align: center;"><span class="math-tex">\(n_A={c\over v_A}\)</span></p> </div> <p>NB: We take air to have a refractive index = 1 (as light is not refracted between a vacuum and air).</p> <p><strong>Critical angle: </strong>When light travels from glass to air, it refracts away from the normal. If the angle of incidence is large enough then the angle of refraction will be 90°. The angle at which this happens is called the <em>critical angle</em>.</p> <p><strong>Total internal reflection: </strong>If the critical angle is exceeded, no ray is refracted and all of the light is reflected inside the more optically dense material.</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p>Total internal reflection can be used to reflect light along long <em>fibre optic</em> cables used in:</p> <ul> <li>telephone and broadband communications</li> <li>endoscopy in medicine</li> <li>domestic lighting</li> </ul> <p style="text-align: center;"><img alt="" src="../../../ib/physics/activities/opticfibre.png" style="width: 566px; height: 130px;"></p> </section> <p><strong>Single slit diffraction: </strong>When light passes through a narrow slit (<0.1mm), it can be observed to spread out. Diffraction is optimised when the slit width approximately equals the wavelength of the light (<span class="math-tex">\(\approx 10^{-7}\)</span>m).</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p style="text-align: center;"><img alt="" height="266" src="../../../ib/physics/images/Practicals/diff1.jpg" width="233"></p> </section> <p><strong>Two slit interference:</strong> If light passes through two narrow slits, interference takes place where the light overlaps.</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden"> <p style="text-align: center;"><img alt="" src="../../../ib/physics/twoslitsphoto.png" style="width: 436px; height: 70px;"></p> </section> <p><strong>Polarisation:</strong> Light can be polarised by passing it through a special plastic called Polaroid.</p> <p>Malus' law gives the relationship between the intensity and angle (<span class="math-tex">\(\theta\)</span>) between the polarisers:</p> <div class="box"> <p style="text-align: center;"><span class="math-tex">\(I=I_0\cos^2 \theta\)</span></p> <p><em>I</em> (Wm<sup>-2</sup>) = transmitted intensity</p> <p>I<sub>0</sub> (Wm<sup>-2</sup>) is the incident intensity</p> </div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-purple"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Summary</p> </div> </div> <div class="panel-body"> <div> <p>There are some key differences between progressive and standing waves:</p> <table border="0" cellpadding="0" cellspacing="0" style="width: 50%;"> <tbody> <tr> <td><strong>Progressive</strong></td> <td><strong>Standing</strong></td> </tr> <tr> <td> <p>Amplitude of all points is equal</p> </td> <td>Amplitude of all points between a node and antinode different</td> </tr> <tr> <td>All points within one wavelength out of phase</td> <td>All points between 2 nodes in phase</td> </tr> <tr> <td>Energy transfer</td> <td>No energy transfer</td> </tr> <tr> <td>Wave profile progresses</td> <td>Wave profile stationary</td> </tr> </tbody> </table> </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 flashcards to practise your recall.</i></p> <div class="tib-flashcard"><a class="show-flashcards btn btn-success btn-xs-block btn-block " data-levels="1" data-mode="Normal" data-topics="530" data-subject-id="6" data-n-flashcards="27" style="text-align:center">Show flashcards</a></div><hr> </div> </div> </div> <div class="panel panel-has-colored-body panel-red"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Just for Fun</p> </div> </div> <div class="panel-body"> <div> <p><em>Check out this πg physics summary.</em></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/389471208"></iframe></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="page-container panel-self-assessment" data-id="278"> <div class="panel-heading">MY PROGRESS</div> <div class="panel-body understanding-rate"> <div class="msg"></div> <label class="label-lg">Self-assessment</label><p>How much of <strong>Waves</strong> have you understood?</p><div class="slider-container text-center"><div id="self-assessment-slider" class="sib-slider self-assessment " data-value="1" data-percentage=""></div></div> <label class="label-lg">My notes</label> <textarea name="page-notes" class="form-control" rows="3" placeholder="Write your notes here..."></textarea> </div> <div class="panel-footer text-xs-center"> <span id="last-edited" class="mb-xs-3"> </span> <div class="actions mt-xs-3"> <button id="save-my-progress" type="button" class="btn btn-sm btn-primary text-center btn-xs-block"> <i class="fa fa-fw fa-floppy-o"></i> Save </button> </div> </div></div> <div id="modal-feedback" class="modal fade" tabindex="-1" role="dialog"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <h4 class="modal-title">Feedback</h4> <button type="button" class="close hidden-xs hidden-sm" data-dismiss="modal" aria-label="Close"> <span aria-hidden="true">×</span> </button> </div> <div class="modal-body"> <div class="errors"></div> <p><strong>Which of the following best describes your feedback?</strong></p> <form method="post" style="overflow: hidden"> <div class="form-group"> <div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Recommendation"> Recommend</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Problem"> Report a problem</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Improvement"> Suggest an improvement</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Other"> Other</label></div> </div> <hr> <div class="row"> <div class="col-md-6"> <div class="form-group"> <label for="feedback-name">Name</label> <input type="text" class="form-control" name="feedback-name" placeholder="Name" value=" "> </div> </div> <div class="col-md-6"> <div class="form-group"> <label for="feedback-email">Email address</label> <input type="email" class="form-control" name="feedback-email" placeholder="Email" value="@airmail.cc"> </div> </div> </div> <div class="form-group"> <label for="feedback-comments">Comments</label> <textarea class="form-control" name="feedback-comments" style="resize: vertical;"></textarea> </div> <input type="hidden" name="feedback-ticket" value="082b9c9c4ae3624d"> <input type="hidden" name="feedback-url" value="https://studyib.net/physics/page/278/waves"> <input type="hidden" name="feedback-subject" value="6"> <input type="hidden" name="feedback-subject-name" value="Physics"> <div class="pull-left"> </div> </form> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary btn-xs-block feedback-submit mb-xs-3 pull-right"> <i class="fa fa-send"></i> Send </button> <button type="button" class="btn btn-default btn-xs-block m-xs-0 pull-left" data-dismiss="modal"> Close </button> </div> </div> </div></div> <div id="fc-viewer" class="modal fade modal-flashcard" tabindex="-1" role="dialog"><div class="modal-dialog" role="document"><div class="modal-content"><div class="modal-header" style="background-color: #fafafa;"><div class="row" style="width: 100%;"><div class="col-md-12 tags-heading"><div style="display: flex; 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