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Ch 17: Superposition

Chapter 17, Problem 17

The fundamental frequency of an open-open tube is 1500 Hz when the tube is filled with 0°C helium. What is its frequency when filled with 0°C air?

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Hey, everyone. So this problem is dealing with frequency in an open pipe that is open at both ends. So let's see what they're asking us. We initially have a pipe filled with neon gas at zero degrees Celsius and a fundamental frequency of 980 Hertz. The next step, this engineer fills the pipe with nitrogen at the same temperature. And now we're asked to determine the frequency of that pipe when it is filled with the nitrogen, they give us the speed of sound um in both nitrogen and neon. So our multiple choice answers here are a Hertz B 524 Hertz C 688 Hertz or D 799 Hertz. So the first thing we can do for this problem is recall that our frequency in a pipe or tube that is open at both ends. It's given by the equation and V divided by two L. Now we are working with fundamental frequencies which means N is equal to one. And so that just goes away. So then our equation is F equals V divided by two L. We are asked to find the frequency of the nitrogen. We have the speed of the nitrogen, but we don't have the length, the length of the pipe, however, is not changing. So we can use the data found for with the neon gas to find the length and then we can find the frequency of the nitrogen gas. So that will be length is equal to the speed of the neon gas divided by two multiplied by the frequency of the neon gas. We were told in the problem that the speed of sound in neon gas is 433 m per second. And that's divided by two, multiplied by the frequency which we were told. And the problem was 980 Hertz. So the length of this pipe is 0.221 m. Now using that to solve for the frequency of the nitrogen gas, we have the speed of sound and nitrogen was given as 353 m per second divided by two multiplied by that length that we just found 0. m. So the frequency with nitrogen gas in the tube is Hertz. And that aligns with answer choice D. So that's all we have for this one. We'll see you in the next video.
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