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SHs uolsano asuodsal 5141 Baes volsanb jauoue guiow 35341/0 3uou 3 L-04 9! 0 z-01 *92 3 Z-01*Zs 9 0 2-01 : *82 V 0 iunuqliinba wuasar aje € NJO Saiow Auel Mo4 "unuqiinba Ie 0Z N /0 Saiou 870 DiE Qiau 'jauieiuo? 7-0*01 E uI FHZ NiO = saiou SZ 0 pue OZ NJO saiow 01 0 aje aja4 Aiieqiui (6 Joz Hz + (6 )2 NE: (6) HZ N+ (6 J0Z NZ ~(auniu se6 jeapl ue aunsse) pelebisaAU] uoqpeal DuImoilog a4L qulod 0L uopsano IIsano asuodsar SIU aAes IIJM uogsanb Jauloue 01 6ULAOW [MM.DDL DMQUL9 LMUDDOCDLC



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Six sound waves have pressure amplitudes $p_{0}$ and frequencies $f$ as given. Rank them in order of the displacement amplitude, largest to smallest. (a) $p_{0}=0.05$ Pa, $f=400 \mathrm{Hz}$ (b) $p_{0}=0.01 \mathrm{Pa}, f=400 \mathrm{Hz}$ (c) $p_{0}=0.01 \mathrm{Pa}, f=2000 \mathrm{Hz}$ (d) $p_{0}=0.05 \mathrm{Pa}, f=80 \mathrm{Hz}$ (e) $p_{0}=0.05 \mathrm{Pa}, f=16 \mathrm{Hz}$ (f) $p_{0}=0.25 \mathrm{Pa}, f=400 \mathrm{Hz}$

Good day in this question we are given the waves industry. So first we are asked to solve for the speed and transfers waves. So speed in transfers wave is equal to the square root of then shown in the spring, divided by the mass per unit land. So our tension given is equal to need to eat. Point to your done. Our mass is equal 2.5 grabs, Converting two kg. We have 1000 g for one kg is equal to five times 10 to the negative for a kg. Our land given is 50 cm converting to meter. We have one m is 170 m. Therefore 0.50 m. Now substituting the parameters to the transference wave speed we have speed equals 88.2. New done divided by five Time stand to the -4 kg divided by 0.5 m. Therefore the speed of the transfer S wave is equal to 200 97 m/s. No, we are asked to solve already frequencies for each fundamental. So using the figure 22 dash to we have the fundamental for for the fundamental. The first overtone and the second overtime we need to find the frequencies. So for the fundamental Length is equal to 1/2 lambda. Since our land is .5 m Lambda or the wave land is equal to one m. There were substituting the Waveland to the frequency equation of frequency. It was speed divided by the Waveland where our speed is the speed that we got from the previews You have to 97 m/s divided by one m frequency. For the fundamental is equal to 297 Hz. Next for the first overtone racist overtone. Our land is equal to two times one half lambda. Therefore our Waveland or lambda is equal to why five you through this. So solving where the frequency we have speed divided by Waveland. It was 297 The 30 per second invited by .5 eaters. Frequency is equal to 594, Urge and lastly for the second over it all we have second overtone where the length is equal to three times 1 half of them now or the one have loved the is our the stands for the and the dudes therefore our we've learned is equal to 0.33 meat fish. Now solving for the frequency of with us. I was speed divided by B. In England we have 297 m/s Divided by .33 meters frequency for the second, overtone is equal to 891 hurts. Thank you

Solving party of this problem. As we all know that have fundamental is equal to have to minus F one. So just putting the value in this X person 1040 heard minus 7 80 hard so it will be equal to 2. 60 Hard as our answer for party Now I am going to solve the part b. So here I can write the fundamental frequency Have fun is equal to one by to well understood t by and by l so simplifying it for the mass of the string Em is equal to t by four and have fun in square. So just putting the value I can write 1200 Newton by for multiplication 1.6 metre multiplication to 60 herds square. So I'm simplifying it. I get the value of M is equal to 0.0 28 kg. So changing it into Graham I can write their musical to 2.8 g as our and

So this question gives us the vibrational frequency off a mode which I've stubbed. F n equals 780 arts and then it gives us the vibrational frequency off the mode immediately following that. So I've said F n plus one is equal to you 1040 arts. It gives us the length off the string on. It tells us that the string is fixed at both ends. So part of this question asks us for the fundamental vibrational frequency given this information. So you know that the frequency of the string can be defined by the velocity off the way of divided by the So we know that the frequency of the wave could be defined by the velocity divided by the Waveland Lamba. And we also know that because the string is fixed at both ends, that Lambda is given by two times the length of the string because, as we can see, if it's fixed at both ends, we have minimum amplitude on. It will resemble something like this at the fundamental frequency. So the first mode off vibration, so therefore we can construct some simultaneous equations. We can say that the Waveland off the 10th mode is equal to to l divided by n So this is like a general case. And as such, we can also say that Lunda of n plus one is equal Teoh to l over and plus one in these two together in terms of their solutions for end. We concede it n is equal Teoh Well, we have to l over Lambda and however we can say that this lambda is equal to from this equation, we can say that our lumber is equal to the over f just by rearranging that so that's actually equal to two l f over the So we can write this out in terms of the solutions for both Lambda and Land A and plus one. So this becomes and is equal Teoh, We have two times R l which is 1.6 meters times by our frequency, which is well for the for the N case that's going to be 780 hertz on divided by the on camera suiting that ve is the same both the end on end plus one cases on so equating that to the end plus one case you want to solve this equation for end now on. In order to do that, well, we have the same times before, So that would be to L, which is two times 1.6 meters times by f of N plus one, which is 1000 and 40 hearts on. That's also over V. However, we also need to minus one because this fast term here on the right hand side, is just the solution for n plus one. So we need to minus one in order to equate this to the previous end. So we have this simultaneous equation here on do. What we can do is we can solve this. We can solve it for the and so doing that we can see that we're multiplying by V rear and simply just rearranging for it gives us that V is equal. Teoh two times, 1.6 meters times. And then it will be be difference because what we will do is we will take this of minus one to the left hand side by adding one. And then we will minus this term on the left to the inside. So that gives us multiplied by 1040 minus 780 hertz Andi that comes out as 832 meters per second. So what we can then do is go back to our first equation that our frequency is equal to the velocity over the wavelength at the fundamental frequency. So we know that that is larvae. We just worked out as 832 meters per second on our Lunder, which we went house to L, which is two times 1.6 meters. Andi, that comes out as 260 hertz, which is the answer in the textbook. So part B of this question asks us while it says that our tension in the string is equal to 1200 Newtons and asks us to work out the mass off the string. So we know that the fundamental frequency F one is defined as well. We know that it's equal to 260 hearts for one because you about in the previous question and it's going to be equal to you from the equation in the textbook one over to L multiplied by the square root of tea over new where mu is our mass per unit length so is equal to em over El Onda. We therefore want to solve for em. So rewriting that out we concede it 260 hertz which is our fundamental frequency is equal to one over to l roots Attention tee times by the length l the m because, as you can see, having em over L on the denominator will bring the L to the top of the fraction. And so rearranging for em conceive it. M is going to be equal to one over to l F one, which is all 260 hunts that will be squared because M is in the square root multiplied by our attention multiplied by our laugh. So rewriting that out in terms of the numbers that we already know that's equal to you one over two times 1.6 times 260 squared. Why units are in s I form. So you need to you worry about that multiplied by attention which is 1200 Newtons multiplied by the length of our string, which is a 1.6 meters Andi that comes out as in sa units as north points and then we have north north to eight kilograms, which is in turn equal to 2.8 grams eight grams. That is our final answer.

Good day in this question we will be solving for the first few resonant frequency of the given figure 22 dash for So based on figure 22 4. Our L. Is equal to the end. Dynasty speed divided by poor dynasty frequency of the resonance or F. of N. is equal to and times to speed divided by four L. So you see figure 22-4. We know that our end here is just one three U. Five seven and so on. But is uh in danger. So you you see that we know that our initial frequency from is equal to from the previous were given For the fundamental frequency of 95 hurts. Therefore our next our first or our next our second overtone is equal to speed divided by the Waveland. Where we've learned Is equal to 3/4 over four. Or let is equal to 3/4 over for a wavelet. Therefore we that is equal to 4/3. Or we can write these us equal to the N. Times the initial in the injury or initially frequency we can use this or we can simply where for the Second over don't end is equal to three time's D. Of what? So our F two is equal to three Times 95 Hz is equal to approximate the 290 Hz. So we are just as for a phrase phew We will show you for the next over 3rd overtones. So for our third overtone it was being divided by Waveland where land is equal to five. We've been divided by four. Or We went equals four l. divided by five. We can use this to solve this, or we can use the number Of N, which is five F 1. So our 3rd frequency is equal to five times 95 hertz, which will give us equal to 480 Hz. Thank you.


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