By whipping a string up and down, you determine the fundamental frequency to be 4 Hz. If you attached the string to a motorized oscillator and increased the frequency to 28 Hz, how many loops would this standing wave have?

Hey, everyone. Welcome back. So in this problem, we're told that we're gonna flick a string up and down to create some standing waves. So we're gonna determine that the fundamental frequency is 4 Hertz. Remember that the fundamental frequency is the smallest frequency that you have to give a string in order to create a standing wave. It's gonna look something like this. Basically, if I take a string and I sort of attach it on both sides, if I give it a fundamental frequency of 4 hertz, I'm gonna create the 1st standing wave. So in other words, I know that f one is equal to 4 hertz. Now this just means that it's a sort of I only have one node here or I only have one loop, because it's basically gonna kinda look like this. That's what your standing wave is gonna look like. Alright? Now what we're told here is that if we attach it to a motorized oscillator and increase the frequency to 28 Hertz, then we're trying to figure out how many loops the standing wave has here. Now one of the important things to remember here is that the fundamental frequency, the n equals 1, so n equals 1, and that's also how many loops you have. So when n equals 1, you have one loop. If n equals 3, you have 3 loops and so on and so forth. So, really, what we're actually trying to find here is we're actually sort of trying to find n in this case. This is kind of just another way of saying what is n, what's the number of loops that you have. Alright? So let's take a look. We actually know that every single, if we're trying to create standing waves, all of them are gonna be multiples of this sort of fundamental frequency. So we're gonna just gonna use this equation over here, our f n equation. So our f n is equal to n times the fundamental frequency. So we actually basically have what this standing wave frequency f n is. We're told that we're gonna increase it 28 Hertz and create another standing wave, and, really, we're just trying to find what n is, and we all know what the fundamental frequency is. So it's pretty sort of straightforward division problem. We're gonna have the 28 equals n times 4. We do the division, 28 divided by 4, and n equals 7. So, basically, what happens is if you increase the frequency to 7 times the fundamental frequency, you'll end up with another standing wave, but it'll actually have 7 loops. And, basically, what this look like, it'll look like 1, 2, 3, 4, 5, 6, 7. And it's terrible, but, basically, it's gonna look something like this. Right? You're gonna have a bunch of these loops here, and you'll actually see that there's 7 sort of distinct ones as it's sort of, like, oscillating like this. Alright? So this is gonna be f, n. This is actually gonna be f 7, which equals 28 hertz, n equals 7 loops. This is what basically this would look like. Alright? So that's the answer. And if you look through your answer choices, it's gonna be answer choice c oh, I'm sorry. If you look through the answers, it's gonna be answer choice d because that's the n number. Alright? So, hopefully, you got that right. Thanks for watching.

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By whipping a string up and down, you determine the fundamental frequency to be 4 Hz. If you attached the string to a motorized oscillator and increased the frequency to 28 Hz, how many loops would this standing wave have?

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