welcome to the physics classrooms video tutorial on vibrations and waves the topic of this video is the interference of waves and we want to know how can you distinguish between constructive and destructive interference and how can you use the principle of superposition to determine the shape of the wave that results from interference Mr H let's get started interference is the phenomenon that takes place when two waves meet up with one another while moving in different directions along the same medium consider pulse one moving to the right each particle the medium will be pulled upwards by pulse 1 as pulse 1 passes through it let's suppose it meets up with pulse 2 moving to the left each particle in the medium will also be pulled upwards by pulse 2 as it moves through the medium this is the individual influence of each pulse upon the medium but when the two pulses meet up with one another the shape of the medium will reflect the sum of each pulse's influence let's suppose we have pulse 1 moving to the right and meeting up with pulse 2 moving to the left as shown pulse 1 pulls upwards upon each particle of the medium but Paul's 2 pulls downwards upon each particle in the medium and when these two pulses meet up with one another the resultant shape of the medium will be the sum of each pulse's influence when waves interfere there can be locations where the interference is considered constructive constructive interference means that the displacement of the medium is greater than the displacement caused by each interfering wave let's consider pulse one moving to the right and meeting up with pulse 2 moving to the left as their leading edges begin to interfere with one another we would notice that the displacement of the medium is greater than that caused by each individual pulse the more that they begin to interfere or meet up with one another the more that we notice that the displacement of the medium is greater than the displacement caused by each individual pulse when they are completely overlapped or completely interfering with one another the maximum displacement experienced by the medium is equal to the sum of the maximum displacement caused by each individual pulse whenever we have two upward displaced pulses or even two downwards displaced pulses interfering with one another that interference is referred to as constructive interference interference can be destructive if each individual pulse displaces the medium in opposite directions for instance an upward displaced pulse meeting up with a downward displaced pulse would result in destructive interference that is shown here with pulse 1 moving to the right and pulling upwards upon each particle and medium pulse 2 is moving to the left and pulling downwards upon each particle of the medium when their leading edges begin to interfere we would notice that the displacement of the medium is less than that caused by the two individual pulses as they're completely or nearly completely overlapped we would notice once more that the net effect upon the medium is less than that caused by the individual pulses it is possible for an upward displaced pulse to completely cancel the effect of a downward displace pulse and For a Moment In Time the resulting displacement of the medium would be absolutely nothing the principle of superposition states that when two waves interfere the resulting displacement of the medium at any location is simply the algebraic sum of the displacements of the individual waves at that location in other words the resulting wave is simply the sum of the two individual waves put another way it's just arithmetic this table illustrates the idea if pulse 1 pulls upward on the medium with one unit of upward displacement and it interferes with pulse 2 that has two units of upward displacement at that location the medium is displaced upward by three units and if pulse one pulls downward with one unit of displacement and meets up with pulse two pulling downwards with one unit of displacement the medium is displaced downwards by two units if pulse one pulls upward one unit displacement and pulse two downwards with one unit of displacement at that particular location there would be no displacement of the medium finally if pulse one goes upwards with one unit of displacement and pulse two downwards with three units of displacement the medium is displaced downwards with two units of displacement it's just arithmetic when wave one and wave two interfere and you want to determine the resultant shape of the medium you have to apply the principle of superposition it might look complicated but remind yourself it's still arithmetic what you do is you pick a strategic Point like maybe the first point along the medium and from the Middle Line the rest position you count the amount of displacement caused by the Red Wave and by the Blue Wave and then you sum it up and at this point the sum is zero I'm going to go over a little bit to the right along the axis and I'm going to do it again for another point I count how much the Blue Wave goes down and how much the red wave goes down at that vertical position and then I go down the sum of those two amounts I repeat the process again for the various locations along the medium picking enough points that I get a feel for what the resultant shape of the wave would be at the various points I keep counting from the rest position up to the Blue Line the rest position up to the red line and then I sum up these two displacements and I put a dot down on the graph after you've done one complete cycle you get a feel for where the resultant wave would be if you were to draw it on the diagram and you could do it a little faster for the next cycle in the nick cycle and the Nick cycle and then once you have enough points you draw a wave through these points and that's what this purple wave represents the resultant shape of the medium when Wave 1 and Wave 2 interfere with one another to recap the method of determining the resultant shape you pick a few strategic points along the medium then you use the grid to identify the displacement of wave one and of Wave 2 and then you add up the displacements of these two waves to get the resulting displacement at that particular location you repeat the process for several points along the medium until you get enough points that you know what the resultant shape of the wave would look like in this case the interference is constructive at all locations because we have a downward displaced pulse meaning a downward displace pulse or an upward displaced pulse meeting an upward displaced pulse here I'm going to apply the principle of superposition to determine the resulting shape of the medium the so-called resultant wave when the Red Wave in the Blue Wave interfere with one another so starting from rest I count up to the Red Wave and down to the Blue Wave and I take the sum of these two measurements and I put a dot on the diagram at that location I'm going to repeat for several strategic locations along the medium count up to the red count down to the blue sum up the results and put a dot on the diagram continue repeat for several locations until you begin to get a feel for the shape of the resultant wave once you have enough points go ahead and sketch the resultant shape on the diagram and that's shown here with the purple wave now this is an example of destructive interference because at every location along the medium the Red Wave is displaced upward in the Blue Wave downwards or vice versa and that's destructive interference now it's not complete cancellation but it would be if the amount of displacement of the Red Wave Upward at every location was equal to the amount of the Blue Wave downwards such that the effect of one waves displacement on the medium is canceled by the displacement by the effect of the other waves displacement on the medium the result is that for a moment in time there be no displacement as denoted by the purple line on this diagram in this last example the wavelength of the red and the Blue Wave are different and so there are locations along the medium where constructive interference is taking place in other locations where destructive interferences taking place these red arrows and corresponding hash marks indicate the locations where destructive interference is taking place you'll note at each of these locations the Red Wave and the Blue Wave are displaced in opposite directions and these green arrows indicate locations where constructive interference is taking place the red and the Blue Wave are displaced in the same direction in each of these locations either both upward or both downwards now if I took the time to mark on the diagram the sum of the red and the Green Wave at several strategic locations I could determine the shape of the resultant wave and that would be denoted by this purple wave here now if you look carefully at every location of a green arrow the amount of displacement of the purple wave is greater than the displacement of both the Red Wave and the Blue Wave because these are constructive interference locations and if you look at the locations of the Red Arrows where destructive interference takes place the amount of displacement of the resultant wave the purple one is less than the result than the displacement of either the red or the Blue Wave it's at this time in every video that I like to help you out with an action plan a series of next steps for making the learning stick but before I help you out could you help us out by giving us a like subscribing to the channel or leaving a question or comment in the comment section below now for your action plan here are four resources that you'll find on our website I've left links to each in the description section of this video anyone would be great next steps you have a physics simulation on the topic of wave Edition a Minds on physics Mission and a concept Builder which would be great conceptual follow-ups and finally if you need to brush up on a topic always turn to our physics classroom tutorial whatever you do I wish you the best best of luck I'm Mr H and I thank you for watching