BIO Deep-sea divers often breathe a mixture of helium and oxygen ...

Question

BIO Deep-sea divers often breathe a mixture of helium and oxygen to avoid getting the 'bends' from breathing high-pressure nitrogen. The helium has the side effect of making the divers' voices sound odd. Although your vocal tract can be roughly described as an open-closed tube, the way you hold your mouth and position your lips greatly affects the standing-wave frequencies of the vocal tract. This is what allows different vowels to sound different. The 'ee' sound is made by shaping your vocal tract to have standing-wave frequencies at, normally, 270 Hz and 2300 Hz. What will these frequencies be for a helium-oxygen mixture in which the speed of sound at body temperature is 750 m/s ? The speed of sound in air at body temperature is 350 m/s .

Accepted Answer

Hey, everyone. So this problem is dealing with sound waves and frequency. Let's see what it's asking us. Recent studies have shown that sound similar to natural speech can be synthesized using a closed pipe system. The closed pipe system will mimic the human vocal tract. A research team investigating the effects of gas variation on the frequencies of the produced sounds used a closed pipe filled with different gasses at room temperature. In the first experiment, a closed pipe is filled with Argon. A vibrating blade produced two standing waves with frequencies of 345 Hertz and Hertz. The experiment is repeated with hydrogen gas inside that same closed pipe determine the frequencies produced when the closed pipe is filled with hydrogen. And it tells us that at room temperature, the speed of sound for Argon 319 m per second and hydrogen 1270. So our multiple choice answers here are a 8.7 times 10 to the one Hertz and 4.23 times 10 to the three Hertz B, 3.45 times 10 to the two Hertz and 1.69 times 10 to the three Hertz C 1.37 times 10 to the three Hertz and 6.71 times 10 to the three Hertz MD, 2.74 times 10 to the three Hertz and 1.34 times 10 to the four Hertz. OK. So the first thing we can do is recall, our frequency equation is given by speed divided by wave length or V over lambda. And in turn lambda for a um open close system is four L. And that, so that really when we pull that together for the different harmonics or N, we have F of N equals N V over four L for this closed pipe system. Now, we don't know the length of the pipe and we don't know which harmonics we, these frequencies are on. But we do know or we can know that the frequencies, the harmonics that they are on are going to be the same whether it's in gas, whichever gas it's in. So we can just call N A really any variable and solve four simultaneous equations between argon and hydrogen. So for the first homo that we're calling a, that's scenario one. So our frequency of A on is equal to a times the speed of argon. For the speed of sound in argon divided by four L four, the frequency of argon divided by the speed of sound in argon is equal to a divided by four for hydrogen, the frequency of hydrogen in the same, for the same scenario for the same harmonic is going to be a multiplied by the speed of sound and hydrogen divided by four L. And so now we see we have this a divided by four L and we can substitute for our um frequency and speed of argon. So that will be frequency of argon multiplied by the speed of sound and hydrogen divided by the speed of sound. And argon is going to be the frequency of hydrogen. Yes, or what to plug in those values at 345 Hertz and the speed of sound and hydrogen 1270 m per second multiply those divided by the speed of sound and Argon 319 m per second. Love that and, and we get 1.37 times 10 to the third part. Now looking at our multiple choice answers that only leaves answer choice C as a as the correct answer, but we can solve for that second frequency just to make sure that we're on the right track. And so it's going to be the same, I it's going to be the same idea where when we have this scenario two or we have this second, higher frequency are higher hydrogen frequency is going to be the higher ARGO frequency that was 1685 Hertz multiply by the seed of sound in hydrogen. 1270 m per second divided by the speed of sound and Argon 319 m per second. You plug that into our calculator and we get 6. times 10 to the third, right? And we go back to multiple choice answers and that does align with answer choice. C so C is the correct answer for this problem. So that's all we have for this one. We'll see you in the next video.

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