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Problem 76 Medium Difficulty

A guitar string is supposed to vibrate at 247 $\mathrm{Hz}$ , but is measured to actually vibrate at 255 $\mathrm{Hz}$ . By what percentage should the tension in the string be changed to get the frequency to the correct value?


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Chapter 15

Wave Motion

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October 8, 2021

Is the string vibrating sharp or flat?

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Video Transcript

we have to get her streams. That is supposed, um, to vibrate at 247 Hertz, but instead it vibrates and 200 55 hurts. So the pitch is higher than we hoped. And that is because if this insolence and the way Flint as a frequency has relationship off equals the over, Linda and Linda could be half of L. Or it could be like to L. A. Or like our or have a veil. Let's say it's a far better frequencies, so Lamda equals to L. But pretty much what we're trying to say is that frequency will be proportional to attention divided by you. And because autopsies will not change, frequency is proportional to the square it optician. So frequency one over frequency to equals a screw it attention one over attention to. So let's say one is, um, what we want and two is that's the one is. What we want into is what it's actually collaborating at. So then what we want is F one, and it equals two. If two terms, if one over f too. It's quick. So, um so force is does it tell us what the forces it did not have what supports it? So I just quit after you on f want iss? What we're hoping for is 227 birds have to what it actually vibrates is 255 words square. This gets us 0.938 after so we won't you decrease attention by roughly 6.2%.

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