2/18/2024 0 Comments Sound diffraction math problemsIn other words, the sound gets louder as you block one speaker! Equally as strange, if you now block one speaker, the destructive interference goes away and you hear the unblocked speaker. If we stand in front of the speakers right now, we will not hear anything! This must be experienced to really appreciate. Now imagine that we start moving on of the speakers back:Īt some point, the two waves will be out of phase – that is, the peaks of one line up with the valleys of the other creating the conditions for destructive interference. If we stand in front of the two speakers, we will hear a tone louder than the individual speakers would produce. If we place them side-by-side, point them in the same direction and play the same frequency, we have just the situation described above to produce constructive interference: The simplest way to create two sound waves is to use two speakers. We shall see that there are many ways to create a pair of waves to demonstrate interference. One wave alone behaves just as we have been discussing. The most important requirement for interference is to have at least two waves. We will explore how to hear this difference in detail in Lab 7. Given the fact that in one case we get a bigger (or louder) wave, and in the other case we get nothing, there should be a pretty big difference between the two. How could we observe this difference between constructive and destructive interference. Phase, itself, is an important aspect of waves, but we will not use this concept in this course. Similarly, when the peaks of one wave line up with the valleys of the other, the waves are said to be "out-of-phase". Although this phrase is not so important for this course, it is so commonly used that I might use it without thinking and you may hear it used in other settings. Often, this is describe by saying the waves are "in-phase". When the peaks of the waves line up, there is constructive interference. The sum of two waves can be less than either wave, alone, and can even be zero. In fact, at all points the two waves exactly cancel each other out and there is no wave left! This is the single most amazing aspect of waves. When the first wave is down and the second is up, they again add to zero. Now what happens if we add these waves together? When the first wave is up, the second wave is down and the two add to zero. However, carefully consider the next situation, again where two waves with the same frequency are traveling in the same direction: You may be thinking that this is pretty obvious and natural – of course the sum of two waves will be bigger than each wave on its own. The waves are adding together to form a bigger wave. This situation, where the resultant wave is bigger than either of the two original, is called constructive interference. If we add these two waves together, point-by-point, we end up with a new wave that looks pretty much like the original waves but its amplitude is larger. To start exploring the implications of the statement above, let’s consider two waves with the same frequency traveling in the same direction: As it turns out, when waves are at the same place at the same time, the amplitudes of the waves simply add together and this is really all we need to know! However, the consequences of this are profound and sometimes startling. Thus, we need to know how to handle this situation. This is very different from solid objects. In the last section we discussed the fact that waves can move through each other, which means that they can be in the same place at the same time. Constructive and Destructive Interferenceĥ.2 Constructive and Destructive Interference
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