파동 주파수, 속도 및 파장 관계 이해하기

### 파동 주파수, 속도 및 파장에 대한 이해
* 🔄 주파수: 초당 주기(헤르츠) 단위로 측정되는 어떤 일이 발생하는 속도입니다. **1헤르츠는 초당 1사이클**이며, 주파수가 높을수록 초당 더 많은 사이클을 의미합니다.
* 🏃 파동 속도: **주파수가 아닌 매체에 의해 결정**됩니다. 주파수가 다른 파동은 동일한 매체에서 **동일한 속도로 이동**합니다.
* 📏 파장: **파도의 두 해당 지점 사이의 거리**(예: 볏과 볏 사이)입니다. 주파수와 반비례 관계: **주파수가 높은 파동은 파장이 짧습니다.**
* 🔁 주파수(f)는 속도(v)를 파장(λ)으로 나눈 값, 즉 **f = v/λ**와 같습니다.
* 🛣 짧은 차량(고주파)은 같은 속도로 움직이는 긴 차량(저주파)보다 **톨게이트 광장을 더 자주 통과**합니다.
* 🧮 공식 조정: **f = v/λ**이지만, 파장은 **파동 속도를 주파수로 나눈 결과**라고 말하는 것이 더 정확합니다.
* 🚀 파동 속도의 변화는 주파수에 영향을 주지 않고 **파장에만 영향을 줍니다.** 주파수는 전적으로 **파동의 소스에 의해 결정**됩니다.
* 📝 연습 문제: **주파수, 속도 및 파장 관계**에 대한 이해를 테스트하기 위해 제공됩니다.

파동은 파장이 짧을수록 주파수가 높지만, 파동 속도는 여러 주파수에 걸쳐 일정하게 유지됩니다.

[Music] Hey everybody, today we are going to talk about wave frequency, speed, and wavelength. Let's start with frequency. So, frequency is the rate at which something occurs. So, if we had a quiz every week, we could say our quiz frequency is one quiz per week. When we're talking waves, we talk about cycles per second or waves per second, which means how many wavelengths occur every second. Now, a cycle is equal to one full wavelength, and a cycle can be measured from a point on one wave to the same point on another wave. And so, that means you would measure either from crest to crest, or you could measure from trough to trough, or really anywhere in between, as long as the two points that you pick are the same points on each wave. Now, we refer to cycles per second in the unit of hertz. So, one hertz is one cycle per second, and that's the number of waves that happen over the number of seconds. So, a couple of examples: if I have one full wavelength that happens in one second, then the frequency of that wave

is one cycle per second or one hertz. If I have two full wavelengths in one second, then we would say the frequency of this wave is two cycles every second or two hertz. Now, I can have partial waves too. It's not always full waves that we get. So, if I have one half of a whole wavelength in one second, I would say that that has one half or 0.5 cycles per second or 0.5 hertz. And if I have one full wavelength in 2 seconds, it works out to be the same 0.5 cycles every second or 0.5 hertz. So, taking the number of waves divided by the number of seconds will give you the number of hertz or cycles per second. So, do a couple of practice problems. If three waves pass by in three seconds, what's the wave frequency? And so, we take three waves divided by three seconds, and that gives us one cycle every second or one cycle per second, which is one hertz. If half of a wave passes by in two

seconds. What is the wave frequency? It's the same process: one half of a wave divided by two seconds of time gives us 0.25 or one-quarter cycles per second or 0.25 hertz. Now, what is it that determines the frequency of a wave? For this, we're going to go to the FET simulation and try some things out. Alrighty, in my simulation, I can adjust a few things. I can adjust the amplitude. I can adjust the frequency. I'm going to leave everything else the same. So, in terms of our start, I'm gonna set this to a frequency of one hertz. That means one cycle every second. And when I give this wave a little amplitude, we get our waveform. Now, notice what is causing the wave. It is this device over here. Now, does that have an effect on frequency? We need to find out by turning the frequency up. So now, I want three cycles every second, not just one. I want more waves every second. I'm gonna juice this up to three hertz, and look what happens to

our wave source, our source of energy, it is now moving faster. So yes, the source of our waves is the cause of the frequency. It is what determines the frequency of a wave. Now, does higher frequency mean that the waves are moving faster? Let's go back to the sim and try something else. All right, at the top we have a three hertz frequency wave, on the bottom we have a one hertz frequency wave. So the top, we're going to get more waves per second crossing that through that point than we will on the bottom. But if you take a look at the crests of the top wave and the crest of a bottom wave, you'll notice that they are moving at the exact same speed. So wave speed does not vary when frequency changes. In fact, if a wave and another wave are going through the same material, they're going to be traveling at the same speed. What changes the frequency is the amount of oscillations every second by the source. In this example, waves of different frequencies are being generated in the

same medium a spring even though the waves are different frequencies. If you watch the crest of both waves, you'll notice they move the exact same speed because it's the medium that determines wave speed, not the source. So just to reiterate, higher frequency does not mean faster waves. Wave speed is determined by the medium, which is the stuff that the wave is moving through. Wave speed does not change with frequency. If wave speed changes, that's because the medium that the wave was traveling through changed. Now what happens if wave speed does change? Does the frequency of the wave change at that point? Let's go to the sim again and try something else. In this example, we have a faster wave on the top part of the screen and a slower wave in the lower part of the screen. Notice though that the frequency is the same. Again, frequency is determined by the source of the wave, and you can see the piston in both screens oscillating at the exact same rate and the same number of waves crossing through the window as well. Here's another simulation when

the wave crosses a boundary into a new medium and speeds up. The frequency of the source doesn't change; the wavelength simply gets longer. If the wave slows down, the waves get shorter. Either way, the same number of waves pass a point each second. So again, if wave speed changes, frequency still does not change. The only thing that determines frequency is the source of the wave. If the wave speed changes, then the wavelength changes proportionally. So just how are frequency and wavelength related? Let me show you a quick analogy involving cars. Let's take a look at two waves: one has a longer wavelength and one has a shorter wavelength, and we're going to relate these to cars. So we're going to say that the shorter wavelengths are like short cars and the longer wavelengths are like longer cars. Let's say we are going to cross a bridge, and we have a line of these cars waiting to pay their tolls. Now both lines are moving at the same speed, and you'll notice that the shorter cars can pass through

at a higher frequency because they're shorter. They don't take as long to pass through the toll plaza. Waves work in a similar way. Higher frequency waves are going to be shorter than lower frequency waves. In order for more waves to pass by per second, higher frequency waves would have to be shorter. Lower frequency waves, just like the longer cars, don't pass by as often due to their longer wavelengths. So, assuming speed is constant, higher frequency waves will have shorter wavelengths and lower frequency waves will have longer wavelengths. So, for a given frequency, we can expect that number of waves to pass by each second. This means that if the speed of the waves changes, the wavelength must also change in order for the same number of waves to still pass by each second. In other words, the ratio of the wave's speed to the wave's length is always the same. For a given frequency, it's accurate to say that the frequency of a wave measured in hertz is equal to the speed of the wave or the velocity of the wave.

measured in meters per second divided by the wave's length measured in meters. Now writing at frequency equals velocity over wavelength almost makes it sound like the frequency is due to the velocity of the wave and its wavelength. But we know the frequency is actually due to the source of the wave in the first place. So we should really rewrite the formula as the wavelength is the result of the wave's velocity divided by the frequency of the wave from the source. This makes a little more sense as to what actually happens. In order to have a wavelength, we need to have a wave. In order to have a wave, we have to have a source in the first place. So writing it in this way makes a little more sense in terms of how things actually work. We start with a wave source that provides energy at a certain frequency, and that energy travels through a medium at a certain speed. The result of those two things gives us a wave that has a particular wavelength. Here's some practice problems. Make sure you pause so you can try the problems before the

answers pop up. There will be a little bit of a delay, so don't worry. You can pause now if you'd like to try these out. All right, here's a little bit of a summary to help you out. Feel free to pause so you can write stuff down. If you have any additional questions, please do not hesitate to ask. Thanks for watching. Have a good one.

Waves - Frequency, Speed, and Wavelength (NEWER vid)

Jon White

주파수는 초당 주기 또는 헤르츠 단위로 측정되는 주기가 발생하는 속도입니다.

1헤르츠는 초당 1주기에 해당하며, 전체 파동과 부분 파동 모두 주파수에 기여할 수 있습니다.

파동 수를 초 수로 나누면 헤르츠 단위의 파동 주파수가 결정됩니다.

파동 주파수는 헤르츠 단위로 측정되는 초당 주기 수에 의해 결정됩니다.

파동의 소스는 주파수를 결정하는 데 중요한 역할을 하며, 소스 이동이 빠르면 초당 더 많은 파동이 발생합니다.

그러나 동일한 물질을 통과하는 파동은 동일한 속도로 이동하기 때문에 파동 속도는 주파수에 관계없이 일정하게 유지됩니다.

파동 속도는 소스가 아닌 매체에 의해 결정되며 주파수에 따라 변하지 않습니다.

파속이 변하면 파장은 그에 비례하여 조정되지만 주파수는 일정하게 유지됩니다.

주파수와 파장의 관계는 짧은 파장은 짧은 자동차, 긴 파장은 긴 자동차에 비유하여 설명할 수 있는데, 둘 다 같은 속도로 움직이는 자동차에 비유하면 파장이 짧으면 짧은 자동차, 파장이 길면 긴 자동차에 해당합니다.

고주파는 파장이 짧고 더 자주 지나가는 반면 저주파는 파장이 길고 빈도가 적습니다.

파도의 속도는 일정하므로 초당 통과하는 파도의 수를 동일하게 유지하려면 속도가 변하면 파장의 변화가 필요합니다.

파장에 대한 공식은 파도의 속도를 주파수로 나눈 값에서 파생되며, 주파수를 결정하는 데 있어 파원의 중요성이 강조됩니다.

답변이 표시되기까지 약간의 지연 시간이 있으니 걱정할 필요는 없습니다.

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발표자는 추가 질문이 있으면 언제든지 답변할 수 있으며 시청해 주신 시청자에게 감사드립니다.