18. Waves & Sound
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Hey, guys. In this video, we're gonna talk about beats and beat frequency beats or things that appear due to interference between two sound waves that occupy the same space at the same time. So this is just another topic on interference, which we've talked about a bunch of times before. All right, let's get to it. When two sounds occupy the same place at the same time, they interfere just like any two waves that occupy the same place at the same time. Alright, Now I drew to sound waves right here. This I put y versus t. But this should technically be pressure versus T. Because sound is a longitudinal wave. It doesn't have a vertical displacement, and they have very, slightly different frequencies is you can see because they start sort of in phase, and then eventually they're out of phase, and then they're sort of back in phase, and then they're out of phase again. That forms this looking graph right here. All right, this piece right here, where the Interfered wave has zero, um, displacement in the pressure graph. Ah, maximum displacement. And then back to zero. This is referred to as a beats. Okay, And if I would have drawn these over many, many, many, many different cycles, many periods, you would see multiple of these beats continue to reappear. You can see half of beat right here, and then you have the other half of the beat over here. Okay, now the interfered waves or composer repeating you. And it's like I said called beats. Beats have two components. You have a high frequency component where you can see the rapid oscillation going on within the beat. Okay, but beats also have a low frequency component, which is the beats themselves. All right, you can see that how long it takes for a whole beat to occur this period right here, this period right here. It's obviously a much, much larger period than the period of these tiny oscillations in here, which occur much, much more rapidly and thus have a much, much smaller period. Okay, The smaller the period, the larger the frequency so beats air composed of those two things a low frequency component and a high frequency component. The low frequency component, which is known as the beat frequency, is given by the difference in the two frequencies that make up the beats. Okay? The reason why I beat frequency is important is because the remember the intensity of sound is dependent upon the largest pressure. Okay, the maximum pressure. Right? The intensity looks something like one half times the maximum pressure. Divided by the density times the speed. So the larger the pressure, the larger the intensity. So the loudest sound in this beat is going to be the sound right here at that peak intensity. So notice. How long does it take between those really, really loud sounds? That's the low frequency part that we were talking about. So the low frequency part is the part that we care about because that's when you hear the sound. Okay, Now that occurs at this frequency F one minus f two. Okay, remember, each beat is a point of maximum displacement, since the volume of sound is directly related to this large pressure. As I said, this is the point where the sound is loudest. Okay. What? The listener here is this is called the beat. Frequency is kind of like a wal wal. Want sound. Okay. Those wands, those air, the high pressure, loud parts to the beats where you'll have beats that look like this or they have the high frequency component. But what you here are those maximum pressure points, and those were the low frequency components. These have the large period where the frequency is given by F one minus F two, but the absolute value because you can't have negative beat frequencies. Okay, let's do an example to illustrate this point. The tuned low e string on a guitar emits a sound of 82 hurts. If you were to strike a tuning fork, which admitted it sounded exactly 82 hurts and you plucked an un tuned low e string. You hear a beat frequency of four hurts. What possible frequencies could your un tuned low E string be at? So you want to get it from whatever it's un tuned? Frequency is to the properly tuned frequency, okay, and this is the most popular way To tune The guitar is to play a sound or really any stringed instrument. And possibly any instrument is to play a sound that you definitely know to be the correct tone. The correct frequency. Play the UN tuned note and listened for the beat frequency and adjust until there's no more beat frequency. But for now, our beat frequency is for hurts. That means that there are two possible values. It could either be 82 plus four, which is 86 hertz. Or it could be 80 to minus four, which is 78 hurts. This comes from the equation for beat frequency. Remember that beat frequency is the absolute value of F one minus two. Okay, 82 86. Air separated by four. But 82 78 are also separated by four. Okay, so these were the two possible frequencies it could be at without changing anything to the problem. Leaving the problem Exactly. It is you cannot possibly know which of those two frequencies is the right one. Alright, guys, that wraps up this introduction to beats and beat frequency. Thanks for watching
A string emits an unknown sound. You strike a tuning fork which emits a sound at EXACTLY 300 Hz, and you hear a beat frequency of 20 Hz. You then tighten the string, increasing the tension in string. After you pluck the string and strike the tuning fork, you hear a new beat frequency of 30 Hz. What is the unknown frequency of the string, originally?
Additional resources for Beats
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