Hey guys. So in the last couple of videos, we took a look at the equation for waves speed for waves on strings, which is really just this guy right here. Well, in some problems, they're going to give you initial setup of a problem. So for example, we have an oscillating blade that's creating transverse waves on a stretched string. And what what they're gonna do in different parts of the problems is they're going to change some of the variables. So for example, in part A, we're gonna call drupal the tension in part B, we're going to double the frequency and they're going to ask you to calculate what happens as a result of this change. So we're going to calculate the new wave speed and the new wavelength. Now in these problems, it's often difficult to understand which variables affect others inside of this equation here. So I'm going to show you how this works. I'm gonna give you some very simple rules for solving these problems. Let's go ahead and check this out here. We're going to start off with part A. So our setup here tells us that we have an oscillating blade which is really just a little blade that's attached to the string that's on a motor that's, that's vibrating up and down. It's creating waves at a frequency of 35 Hertz. So it's basically spinning up and down at a frequency of 35. We're told the tension on this string here is 98. We're also told that the mass density of this is true is just two. And initially, we calculate the wave speed. So this whole entire wave is moving to the right with 7 m per second. And we're also told that the wavelength this lambda here is equal to 0.2. Now you can just trust me on that or you can actually plug in all the values inside of this equation and you actually get those numbers. So in part A, we're going to quadruple the tension on the string and then we want to calculate the new wave speed. So basically what they're saying here is I'm going to calculate this uh this, this new tension in which I'm gonna call ft prime. It's just gonna be quadruple what the initial tension was. So it's gonna be four times 98 which is equal 392. And now we want to calculate the new wave speed. So I'm gonna call this va and that brings us to the first rule. The first rule to solve these problems is that the velocity, remember depends on the mass the, the, the sorry, the tension, the mass and the length, it depends on the physical properties of the medium. So anytime you change any one of these values, tension mass or length, you're always going to change the velocity. So remember to change any one of these values here, like the tension or the mass and the l it's going directly impact the speed of the wave that's on the string. So what happens is to calculate our new velocity? All we have to do is just use this same equation here. But now we just have to use our updated or a new value for tension. So we're just going to use the square roots of FT prime divided by the mu. Now FT prime is the only one that's changed. Now, we just have 392 and our new value hasn't, it's just two, right? The mass and length hasn't changed. So what you end up getting here is you get getting 4 14 m per second, which is exactly twice what the initial wave speed was. I'm gonna call this V knot here. And that's because we quadruple the value that's inside this numerator. So effectively, we are doubling the wave speed. All right. So that's the, that's the first rule. Let's take a look. Now at the second part of the problem. Now we're going to double the frequency of the oscillator. So what happens here is remember that we have this little spinning blade that's oscillating, vibrating up and down. And all that happens is that now we're going to increase that, we're gonna double it. So what happens is we're gonna move this, this vibrating blade and it's gonna go faster. It's gonna create these little bunched up waves like this. We want to do the same thing here. We want to calculate the new wave speed and also the new wavelength. So now what happens is we have our new frequency F prime is going to be twice the original frequency. So I'm going to call this original frequency 35 Hertz. So we just have two times 35 which equals 70. And now we want to calculate the new wave speed. I'm gonna call this VB and I'm gonna call this lambda B. So now what happens is we're going to take a look at our second rule. Our second rule says that the frequency of a wave depends only on the oscillator frequency. So what happens here is that this oscillator frequency is directly going to impact what this F is. So I'm going to call this F oscillator, which is really what this is and these things are equal to each other. So whatever this is, that's going to be the F that's inside of your problems. Now remember that the frequency of the wave speed depends only on the physical properties of the medium tension mass and length. So because F depends only on the oscillator frequency changing, it does not affect the velocity, changing the oscillator frequency only affects F and LAMBDA. So what happens is any change that you make to, this is going to directly impact the F, it's not going to impact the V string. So what happens as a result? Well, basically, if F has to increase or decrease, then that means that your wavelength is going to have to decrease or increase proportionally because this V has to remain the same. That's what the rule is. So what this means here is that by changing the oscillator frequency, your wave speed actually doesn't change at all. So VB is just the initial wave speed which is going to be 7 m per second. And that's the answer your wave speed does not change at all. So what happens to the wavelength as a result? We can actually just go ahead and calculate this by using this equation here string equals lambda. F. If you solve this lambda, which you're gonna get is VV initial divided by the new frequency which you're going to get here is the 7 m per second divided by the new frequency of 70 you're gonna get a wavelength that's 0.1 m. So this actually makes some sense. If you're doubling the frequency of the oscillator, you're going to create these or bunched up waves like this. And that just means that the wavelength is gonna decrease because now you're gonna be creating more bunched up waves like this, the wave speed remains the same, your frequency increases, but your wavelength is going to decrease as a result. Now it's 0.1 whereas initially it was 0.2. All right. So that's how these problems work. Let me know if you guys have any questions.