Hey it's professor Dave, let's talk about interference and diffraction. We know a bit about wave mechanics now, so it's time to look at some wave related phenomena, like what can happen when two waves overlap, or when a wave runs into some solid surface. These are very common occurrences, as we are frequently experiencing sound from more than one location at once, and sound will bounce off of walls and other surfaces, so we need to understand what happens to waves in these scenarios. We know that two solid objects like two people can't occupy the same space at the same time. But mechanical waves are not matter, they are displacements of matter that carry energy, so two waves can occupy the same space, and when two waves combine in this way it is called superposition. When there are two disturbances near one another and their respected series of waves overlap, this is called an interference pattern, and we can see how the regions where the waves intersect generate a completely new pattern. This is easy to see with waves in the water but sound and light waves also do this. There are a few different things that can happen when interference occurs. Say two individual wave pulses are traveling towards each other and they have the same amplitude. When these meet, the amplitudes at each point will be added together to produce the respective points on the resultant wave, so there will be a moment where there is one wave with twice the amplitude. Then the two waves continue in the direction they were moving. Each wave maintains its own characteristics before and after the interference. When a resultant wave has greater amplitude than the individual waves, like this case, this is called constructive interference. Now let's say the pulses are on opposite sides of the equilibrium position. Again, according to the superposition principle, we will add the amplitudes to get the resultant wave, but in this case the two amplitudes add to 0, so the resultant wave will be as though there is no wave at all. Then the waves continue along their trajectories. This kind of interference, where the resultant wave has a smaller amplitude than the individual waves, is called destructive interference, and if the resultant wave has an amplitude of zero, like this example, it is called complete destructive interference. This concept applies to periodic waves as well. First, we can consider two sine waves that are precisely aligned. They are said to be exactly in phase. We can add the amplitudes at every single point and the result is a similar-looking wave with twice the amplitude, due to constructive interference, because the crests align with the crests and the troughs align with the troughs. But then if we shift one of these by half its wavelength, now the crests of one align with the troughs of another, and at every single point on the x-axis these waves will add up to zero. They are said to be exactly out of phase and this will be an example of complete destructive interference. This is what noise cancellation headphones do. Small microphones detect background noise and process the associated signal, and then reproduce this noise in a way that is precisely out of phase with the signal. The resulting destructive interference results in zero, or at least dramatically reduced sound waves reaching your ears. In reality, interference patterns are often much more complicated than these two extremes, but in every case the superposition principle is still applicable. We also want to understand what happens when waves hit a boundary of some kind. If a boundary is free to move, waves will be reflected, bouncing back in the opposite direction but maintaining the same amplitude. If instead this boundary is fixed, waves will be both reflected and inverted, bouncing back in the opposite direction but now with amplitude of the opposite sign. Let's say instead of arriving at a solid boundary, a wave arrives at a boundary with a small gap in it. When waves reach an opening like this they will bend around the edges, producing a phenomenon called diffraction. A diffraction pattern is another kind of interference pattern, because of the series of maxima and minima that result, and waves of all types will exhibit this behavior. It was the diffraction of light that provided some of the strangest data we have collected in physics, contributing to the development of quantum theory, but that will have to wait until the modern physics course. For now, let's check comprehension. Thanks for watching, guys. Subscribe to my channel for more tutorials, support me on patreon so I can keep making content, and as always feel free to email me: