One of the harmonic frequencies for a particular string under tension is 325 Hz. The next higher harmonic frequency is 390 Hz. What harmonic frequency is next higher after the harmonic frequency 195 Hz?

Hey, everyone. Hopefully, I got a chance to try this practice problem. So we're told that one of the harmonic frequencies of a particular string is 325 hertz, and that's one of those standing wave frequencies. We're also told that the next successive higher harmonic frequency is 390. And we're gonna use this information to find what harmonic frequency is next after 195. So we're told a bunch of different numbers here. Let's sort of see if we can sort this out in order and sort of go from lowest to highest and see what's going on here. Now we know that standing wave frequencies, basically, the first one is gonna be your f one. So you're gonna go from 0, and then you're gonna hit some number over here. Now we actually don't know what that f one frequency is, but we do know that later down the line, you are gonna hit 190 95. What we're actually trying to find is, well, the next one that comes after 195. Right? So this is really what we're trying to figure out in the sequence. But then later on, we also know that one of the standing wave frequencies is 325, and the one directly after that is gonna be 390. So can we use this information to figure out what the harmonic frequency is or the fundamental frequency so that we can figure out what's next in line after 190 5. That's really what we're trying to find here. And, basically, what it comes down to is that even though we don't know what the fundamental frequency is because we weren't told that information, We can actually find it basically just by using 2 successive harmonic frequencies that we do know. If we know what the difference between these two frequencies are, we can just trace that back all the way until we get to whatever is after 195. Alright? So what's the difference between these 2? This is basically gonna be your f one. It's just gonna be 390 minus 325. Right? If that's the difference, if these if these two things are are totally successive, then we can basically just take that number, which in this case is 65 hertz, and then we can basically just trace backwards from there, or we can just actually go up from from 0 and figure out all the numbers that go in between. So from 0, you're gonna have 65, and after 65, you'll have, a 130. And then after a 130, you'll actually hit 195. So there it is. That's the 195 we were talking about. So then what's next after that? What's 195 plus 65? Well, Well, if you actually work this out, this is actually just gonna be 260 over here. You also just could have used, basically, once you knew that this was 65, you could just look at the answer choices and figure out that the only one that actually makes sense is 260. Alright? So 195 plus 65 over here is actually going to be your final answer. So this is going to be, answer choice a. Hopefully, that made sense. Thanks for watching.

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One of the harmonic frequencies for a particular string under tension is 325 Hz. The next higher harmonic frequency is 390 Hz. What harmonic frequency is next higher after the harmonic frequency 195 Hz?

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