Understanding Wave Frequency, Speed, and Wavelength Relationships

Waves have higher frequencies with shorter wavelengths, but wave speed remains constant across different frequencies.

### Understanding Wave Frequency, Speed, and Wavelength
* 🔄 **Frequency**: The rate at which something occurs, measured in cycles per second (**hertz**). One hertz is one cycle per second, with higher frequencies meaning **more cycles per second**.
* 🏃 **Wave Speed**: Determined by the medium, not the frequency. Waves of different frequencies travel at the **same speed** in the same medium.
* 📏 **Wavelength**: The distance between two corresponding points on a wave, such as crest to crest. Inversely related to frequency: **higher frequency waves have shorter wavelengths**.
* 🔁 **Frequency (f)** is equal to **speed (v)** divided by **wavelength (λ)**, or **f = v/λ**.
* 🛣 **Shorter cars (higher frequency waves)** pass through a toll plaza more frequently than **longer cars (lower frequency waves)** moving at the same speed.
* 🧮 **Formula Adjustment**: While f = v/λ, it's more accurate to say that **wavelength is the result of wave speed divided by frequency**.
* 🚀 **Changing wave speed** does not affect frequency, only wavelength. Frequency is solely determined by the **source of the wave**.
* 📝 **Practice Problems**: Provided to test understanding of **frequency, speed, and wavelength relationships**.

[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

Frequency is the rate at which cycles occur, measured in cycles per second or hertz.

One hertz equals one cycle per second, and both full and partial waves can contribute to the frequency.

The number of waves divided by the number of seconds determines the wave frequency in hertz.

Wave frequency is determined by the number of cycles per second, measured in hertz.

The source of the waves plays a crucial role in determining the frequency, with a faster source movement resulting in more waves per second.

However, wave speed remains constant regardless of frequency, as waves traveling through the same material move at the same speed.

Wave speed is determined by the medium, not the source, and does not change with frequency.

When wave speed changes, the wavelength adjusts proportionally, while the frequency remains constant.

The relationship between frequency and wavelength can be illustrated with an analogy of cars, where shorter wavelengths are like short cars and longer wavelengths like longer cars, both moving at the same speed.

The Relationship Between Wave Frequency and Wavelength

Higher frequency waves are shorter and pass by more often, while lower frequency waves are longer and less frequent.

The speed of the waves is constant, so a change in speed requires a change in wavelength to maintain the same number of waves passing by per second.

The formula for wavelength is derived from the wave's velocity divided by its frequency, emphasizing the importance of the wave source in determining its frequency.

There will be a slight delay before answers pop up, so there's no need to worry.

Viewers are encouraged to pause the video to write down information.

The presenter is open to answering any additional questions and thanks the viewers for watching.