The fundamental frequency of a pipe that is open at both ends is ...

Question

The fundamental frequency of a pipe that is open at both ends is 524 Hz. (a) How long is this pipe? If one end is now closed

Accepted Answer

Hey everyone in this problem? We have a musical instrument. Okay. It's a long metallic conduit and it's open at both ends. OK. It produces a first harmonic frequency of 250 hertz. And we're asked to find the length of it. Okay. All right. So, the first thing we want to note is that it's open at both ends. OK. So this tells us that this is a node node scenario. Okay. Alright. We also know the frequency. Okay. And it's the first harmonic frequency. So we know F one. There's 250 Hz. All right. So, what's write down what we know about the frequency and maybe that'll help us find the link. Okay, So again, we're no note situation. So we know that the frequency F is going to be given by V over lambda. And Okay. And in this case lambda end is going to be two L. Over N. Alright, so we're talking about F one. Okay, so we want λ one. And if we're looking at λ one, that's just going to be equal to two L. So now we can replace this wavelength λ with two L. And we get that F One is equal to V over two L. Alright. We know F one. We were given in the question 250 Hz. Okay. We know v. We're talking about sound here. So we're using the speed of sound, which we know. Alright. And then we can find L. Which is what we're looking for. Alright. So let's give ourselves some more room and get started with that. So we have 250 hertz. Okay. Is equal to the speed of sound? You can look that up in your textbook um or a table that your professor has provided. That's going to be 343 m per second. Okay. This is hurts. So one over seconds divided by two L. Okay, Multiplying two L. We're going to get 500 l. is equal to 343. Okay. On the left hand side we have one over seconds times L. On the right hand side we have meters per second. And so when we divide we're gonna end up with L. Is equal to 0. m. Okay? So that is the length of the conduit and that is going to correspond with answer A. That's it for this one. Thanks everyone for watching. See you in the next video.

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