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Two open organs pipes of fundamental frequencies $v_{1}$ and $v_{2}$ are joined in series. The fundamental frequency of the new pipe so obtained will be(a) $v_{1}+v...

Question

Two open organs pipes of fundamental frequencies $v_{1}$ and $v_{2}$ are joined in series. The fundamental frequency of the new pipe so obtained will be(a) $v_{1}+v_{2}$(b) $frac{v_{1} v_{2}}{left(v_{1}+v_{2}ight)}$(c) $frac{v_{1} v_{2}}{v_{1}-v_{2}}$(d) $sqrt{left(v_{1}^{2}+v_{2}^{2}ight)}$

Two open organs pipes of fundamental frequencies $v_{1}$ and $v_{2}$ are joined in series. The fundamental frequency of the new pipe so obtained will be (a) $v_{1}+v_{2}$ (b) $frac{v_{1} v_{2}}{left(v_{1}+v_{2} ight)}$ (c) $frac{v_{1} v_{2}}{v_{1}-v_{2}}$ (d) $sqrt{left(v_{1}^{2}+v_{2}^{2} ight)}$



Answers

Two open organs pipes of fundamental frequencies $v_{1}$ and $v_{2}$ are joined in series. The fundamental frequency of the new pipe so obtained will be (a) $v_{1}+v_{2}$ (b) $\frac{v_{1} v_{2}}{\left(v_{1}+v_{2}\right)}$ (c) $\frac{v_{1} v_{2}}{v_{1}-v_{2}}$ (d) $\sqrt{\left(v_{1}^{2}+v_{2}^{2}\right)}$

Okay, so in this problem, we have three different frequencies they're given. And we have to find out whether we have an open pipe or close by. So toe begin. We can see how the waves forming and open by and a close by. So as you can see for an open by Ah, yeah, As you can see for an open pipe you have to Andy notes at the end. And then you have one note for the first harmonic and then for the second harmony, you have two notes and ah, twenty notes eso for unopened by There's all There's always gonna be anti notes at the end and for close by you'LL have one note at the end because it's closed and then on the other and you can have an anti anti note and ah, if you look at the first harmonic and second harmony, the difference between them is so. Second, harmonic is basically twice off the first hard money and for close to five, it's ah three times the first our money. So the difference between the harmonics in in an open five is basically the fundamental frequency which is F one and for close by weights twice off the fundamental frequency. So if on dso in, that's one way to verify if we haven't opened by water close by. So let's look at what we are given. So we have three different frequencies. Ah, and if we take the difference between those preferences so you see the difference between successive overtones off foreign open by is the fundamental frequency as we mentioned on DH then, ah, it should be any determine multiple. So you see, if you take the difference between this excessive frequencies, you will have the differences one seventy six herds. So if you'ii if we divide Teo for sixty four hugs by one seventy six and ah, we see this is not an in teacher, so that means Ah, it is not in India. So that means this is not an open bite. And if it's not an open by ah, it we conclude that this is a close type and ah, so that on DH if we look att Ah, this line over is it says the different between successive overtones for a closed five is twice the fundament frequency. So if we're claiming this is a closed by we can. Ah, very five. We'LL claim whatever. We're claiming it's true or not. So if it's twice the fundament frequency, that means our fundamental frequency will be half off the difference. So if we divide that by two, we get eighty eight herds and so this should be the funding of pregnancy. Now, if you want to verify that we can divide our frequencies by our fundament frequents and see figuring teacher or not. So if we do that ah, we get ah three. If we divide our for forty herds by eighty eight, we get five on DH. If we divide six one six by eighty eight, we get, um, seven. So in that way, we we know that. Okay, this is a close pipe. And ah, we also verify that this is true because we're getting indigent numbers by our fundamental frequency calculation. Thank you.

So here we know the length equals 45 centimeters, or we can say the length is equal to a 450.45 meters now for part A. They want the fundamental frequency such that the pipe is open at both ends, So this will be the velocity divided by two l hear it the velocities that's going to be the speed of sound with an air so 344 meters per second, divided by two times point for five. And this is giving us 382 hertz. Remember that this is for a pipe that is open at both ends. The the 1st 3 overtones will be the second harmonic. This will simply be two times 3 82 so 7 64 hurts. The third harmonic will be three times the fundamental frequency, or 1,146 hertz, and then the fourth harmonic or the third overtone will be equal to four times the fundamental frequency. So 1,528 hurts now for part B. They want the fundamental frequency such that it is closed at one end. So if it's closed at one end That means that the freak that the wavelength is equal to four times the length so it will be the fundamental frequency of the pipe that has closed at one end will be equal to the speed of sound, with an air divided by four times the length or the wavelength. And this will equal 344 divided by four times 40.45 And we're getting 191 hurts. Note that this is exactly half of this of 3 82 And so we can say that the frequency of the first overtone the pipe when the pipe is closed at one end and is not goingto end can only take on odd and treasures not even and odd. So the first overtone is going to be F sub three instead of F sub, too, and this is simply going to be three times the fundamental frequency. So 573 hurts, and then f sub five the second, the second overtone will be equal to five times 191. So 955 hertz and then the fourth overtone well, second through first rather than third overtone will be f sub seven and this will be seven times 191. So 1,337 hertz. So again, 1st 2nd and third overtone now for part. See, they're asking us if if someone can here a frequency of 20,000 hertz. What harmonic is that? So for the open pipe, the harmonic is going to be equal to the frequency of that harmonic divided by the fundamental frequency. So this will be 20,000 hertz divided by 382 hertz, and this is equal in 52. So the highest harmonic that can be heard is the 52nd harmonic and then here closed that one end. This means that and that can only equal f sub and divided by f f the fundamental frequency. However, here it's going to be 20,000 divided by 1 91 and this will be 104 now notice if it's closed at one end and can only take odd integers. So this is an even into jher. Therefore, on equals one less than this. So it becomes alright, Esso and equals 103. So that would be the highest that the Ah, listen, er can hear if the pipe is closed at one end. This would be the highest the listener can hear. If the pipe is open at both ends, that is the end of the solution. Thank you for watching.

Can resonate at 264 hertz 440 hurts. And 616 hertz. But not at any other frequencies in B show. Why is this an open or closed pipe? And B, what is the fundamental frequency of the pipe? So we're given three frequencies at which this pipe can resonate, and I wrote them down. I call him F one F two and a three. Um, and, uh, the differences between successive overtones for this pipe is the difference between two of these frequencies. So we'll write this as Delta F, and it doesn't matter which frequency as long as their successive frequency. So we don't want to do between f three F one but f to F one or a three enough to something like that. So if we do f two minus f one, for example, we find that this is equal to 176 hertz. Oh, okay. So now we know the difference between success of fundamental frequencies because 176 hurts. Okay, but for an open pipe, all right, because I want to know. For part A is an open or closed pipe for an open pipe. One of these fundamental frequencies or one of these? I'm sorry. One of these resident frequencies would be a, um S O F one f to r F three would be an inter jure of this, uh, difference between these resonant frequencies by which we have called Delta F here. So that means Well, Delta F is 176. That means F one has to be interred your multiples of this value. So that means 176 that closest. It could be if it's an integer multiple is too. So but two times Delta F So two Delta F is not equal to F one, and that was a requirement for it to be an open pipes. So therefore, it has to be a closed right so he can box that in. Okay. Well, Part B says, what is the fundamental frequency of this close fight for a close pipe? The success of overtones, which we had found Delta F differ by twice the fundamental frequency. Okay, So that means for part B here that the fundamental frequency is equal to, um, 1/2 Don't. Yes, That's because the success of overtones are equal to the difference between success of overtones is equal to two times the fundamental frequency. So the fundamental frequency has happened. What half Delta F and that equals 88 Hertz. Since Delta F is 176 and half 176 it's 88. Oh, we'll box that in their solution, part B.

The question is asked, What is the beat frequency When we have two tubes, they're different. M pressures. One is 25 degrees and other one is a 30 degrees. And we are asked to find the the beat frequency beat frequency we can find by writing the fundamental frequency off a tube, which is closed at one end. Can be written is if one is equal to of lost e off sound or 40 L is the length of the tube. Since there compressor exchanging that means that we're lost is changing. So then we can right the frequency and 30 degrees or frequencies at 25 degrees will be equal to mmm, the lost city at 30 degrees or the velocity and 25 degrees. We simply plug this value here on four Elkins allowed with four l. So we are only left with the velocities 30 degrees in 25 degrees. Um, then we can find a frequency at 30 degrees in terms off the frequency of 25 degrees. But just cross multiply it and putting the value off, um, velocity off the sound at 30 degrees will be three, um, pre pre one plus zero point six factor times the temperature Some temperature we have is 30 degrees and in denominator we have 17 331 plus is your 0.6 factor. Multiply with 25 degrees. We were asked to find there the beat frequency. So the change in frequency is equal to if 30 regrets it hired him. Preacher minus F 25. So, by changing over by taking the difference and plug in the formula above then the frequency were we get here is 30. Sorry, three hurts. He does so the beach frequency we have, he said. Three hearts end off the problem. Thank you for watching.


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