The figure below shows a standing wave on a 2.0-m-long string that has been fixed at both ends and tightened until the wave speed is 40 m/s. What is the frequency of this wave?

Hey, everyone. So, hopefully, you got a chance to try this problem on your own. But if you're still struggling, just let me go ahead and help you out a little bit. So we're given an illustration for a standing wave that sort of fixed between two ends, like we're given over here. We're also told some information about the string, the fact that it's 2 meters long, and we're also told that the wave speed is 40 meters per second. And, ultimately, what we wanna do is we wanna figure out the frequency of this particular standing wave that we set up over here. So let's get started because we have a lot of new equations here that deal with the frequency of a standing wave. So let's see if we can use them. Alright? So let's get started. So we're asked to find the frequency of the wave. So the most sort of simple equation that you could try to use is the f one equation. So can we use this f one equation? Well, remember that this equation only corresponds to the fundamental frequency. So in other words, this only applies when n equals 1. That's when we can use this. But if you take a look at the wave that we're given here, the standing wave, we actually see that there's 1, 2, 3, 4 loops. Because there's 4 loops, we know that this is the n equals 4, the 4th harmonic frequency. So we can't use this fundamental frequency equation here because that's only f one. Instead, what we can use or we're gonna have to use the more generic sort of, definition or equation for the, frequency, which is this f n equation over here. So we know that f n is just gonna be some kind of a multiple of the fundamental frequency. But because we don't know the fundamental frequency, we can't use this part of the equation. Instead, we're gonna sort of go to the more longer version, which is n times v divided by 2 l. So in this equation, we need 2 things. We need what the wave speed is, and that actually and that which actually is what we do know. We do that we know that the wave speed is 40 meters per second. We also need to know the length of the string, and we actually also know the length of the string because it's given to us as well. So, really, it's sort of just like a plug and chug of this particular equation. The hardest parts of these problems is figuring out which equation you actually need to use. But this is what we're gonna use here. So this is gonna be, we're gonna use n times v. Some of the words, the n is 4. The v that we're given here is 40 meters per second divided by 2 times l. And in this case, the length of the string is 2. Now if you actually work this out, what you're end up get what you'll end up getting is the 4 and the 2 times 2 will actually just end up canceling. And so the fundamental or sorry. Not the fundamental. The 4th harmonic frequency in this case will actually be 40 hertz. Alright? So once your stuff cancels and you'll end up with 40 hertz, you look through your answer choices, and that's gonna be answer choice c. So, hopefully, you got that right. Let me know if you have any questions. Thanks for watching.

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The figure below shows a standing wave on a 2.0-m-long string that has been fixed at both ends and tightened until the wave speed is 40 m/s. What is the frequency of this wave?

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