 So, once you have this then what you can do is you compute this parameter called L w, it is sources acoustic strength and that is basically 10 log p over reference power which is 10 to the power of minus 12, reference is 1 pico watts. So, now this is again a very coarse approach in several machines the manufacturer of the machine will himself provide you this value of p or the value of L w. So, in that case you do not have to resort to this course. So, then based on this if you know that I have 20 pieces of machinery in this whole setup or 20 different sound emitting components and each component you can figure out this is L w 1, L w 2 so on and so forth. Then what I am measuring is some noise spectrum which has certain amplitude at different frequencies then based on that also you can map how much sound is coming from how much noise is coming from which particular component. So, it gives you some course understanding of that. So, with this brief discussion we will talk about noise signatures. So, if I have a fan or a blower we are not talking about ceiling fan fans which pump air then they generate a fundamental frequency F b which equals n times n over 60. So, n is the rpm and n I have it other way n is the rpm and uppercase n is number of blades and this makes physical sense. If I fan 5 blades then each time a blade passes through the opening it pushes air into that thing and if it is doing n times and they are 5 so things then it is 5 n. So, this will be the fundamental tone it will generate then it will have second harmonic third harmonic. So, 2 F b 3 F b and so on and so forth. In case of fan because these generate a lot of noise once we have figured out L w then at this point we also introduce another term called specific sound power level. And this particular parameter helps me compare noise characteristics of one fan with respect to another fan in a normal normalized way. So, essentially it is defined as SPL P standing for not pressure but power sound power level by a fan when it delivers 1 cubic meter of air for every second at 1 kilo Pascal's. So, it is 1 kilo Pascal's above atmospheric air pressure. So, if I have 2 fans totally different fans one is delivering 20 cubic meters at so many Pascal's and this one is delivering some other number of cubic meters at some other pressure level. If I bring it down to this specific sound power level I can figure out how much noise is generated I can compare the noise characteristics of 2 fans. So, on the second table which you have in hand and this is actually a good chart good reference one what you have on table 14.2 are different frequencies actually they are frequency bands. So, you have a frequency band from 63 plus some hertz and 63 minus hertz and the middle frequency point is 63 hertz. So, that is the center point. So, 63 they are 8 bands and for different wheel size and different types of fans you have different values of the sound specific sound power level. Now, you can use this chart to calculate total amount of noise emitted by a fan and we will show that through an example. So, before that I will label this as L W S specific sound power level as L W S. So, if I know the specific sound power level of a fan and if the fan is running at some other RPM no not is emitting or producing air at some other value then L W fan which is the actual noise generated is basically L W S plus 10 logarithm of Q plus 20 logarithm of P T. Q is volume flow rate in meters cube per second and P T is total pressure. This relation is good for all frequencies which are shown in this chart except F B because at F B it will have a peak. So, for all other frequencies if I let us say at 63 hertz 63 hertz I find what is my L W S first case is 85. So, if I have a fan which is axial backward curve over 0.75 then at 63 hertz it generates 85 decibels plus 10 log of Q plus 20 log of P T understood. So, I can use this table to the extent I am not computing SPL at the blade frequency. Now, to compute the SPL at blade frequency the last column you have is called BFI blade frequency index. So, you add that blade frequency index number that is also in decibels. So, this is the over approach. So, we will do a very quick simple example to make things better look more simple. So, let us say a fan has 24 blades rotor dia equals 0.8 meters RPM is 750 flow equals 18 meter cube per second and total pressure is 1.5 kPa. So, my F B is what 750 times 24 over 60 that is 300 hertz. What is L W S for this fan specific sound power level? This fan is radial curved forward. So, in the table if you look forward curved fan what is the L W S which row should I pick the last one forward 98, 98, 88, 81, 81 that row does everyone see that. So, what I will just do is very quickly develop matrix. So, for different frequencies you have 63, 125, 250, 500 and I will not write all other numbers. My L W S for this fan is what can you give me the numbers at 65 hertz or 63 hertz 98, 98, 88, 81 and so on and so forth right. Then my L W S plus 16, where did 16 come from? So, 10 log of 18 plus 10 is it 20 log 20? 20 log 1.5 is 16. So, if I add 16 to this what I get is 114, 114, 104 and 97. So, this is the sound power level if this fan is going to emit for all frequencies except at 300 hertz. So, for 300 hertz what is the adder I have to put? Yeah that B F I which is 2. So, I will change this 250 to 100 and what was the number? 97 plus B F I. So, this is how I compute. So, you understood this right L W S plus 16. So, this is 100 and 104. So, at 300 hertz I have to add 2 dBs more because of this B F I factor right. So, I am just changing this column and I am making it 106. Now, you may also be encountered with a question that. So, you have a fan it has an inlet and it has an outlet. So, you may be wondering how much is contributed by inlet and how much is being contributed by outlet. So, you just split it half and half. So, by inlet contribution is when I do half of it what is what does this number become? This is in decibels and power. So, how much do I should I make it 57 or what do I do? Not 57. 3 dB because power is 10 log something. So, half of this noise is coming from inlet of the fan and half of this noise is coming from outlet of the fan. This is an assumption. So, half of the noise translates to 11111110394 and the other half is coming from. Why do I need to know this? Because now if I have to do some ANC active noise cancellation I can actually place a small transducer in the inlet and it will correct the signals. So, this is the signature for a fan electric motors. This is just to give you a flavor that depending on which type of machinery or components you have you have to figure out what are the noise signatures of different components. So, for this LW is 20 log of power, but we express power in horse powers because most of the motors are rated in horse powers plus 15 log N, where N is the RPM plus KM. Typically, this KM is provided by the manufacturer or it is quite often used as 13 decibels. Transformers does transformer have any moving parts, but still it generates sound. If you go by some of these big transformers on the roads you hear noise, where is it coming from? Sometime it can be appreciable the SPL. But where is that vibration coming from? Even if you put it in vacuum it well not vacuum in still air it will still emit sound. The electromagnetic forces are pulsating based on whatever is your AC frequency and they induce vibrations in the metallic structure. So, if it is a 50 hertz current supply as in India then it is typically twice of that number 100 hertz signal or 120 hertz in country like USA. So, lot of times some of these signatures you can attribute it to transformer. Sometimes you have a PCB which has an inductor on it nothing is moving and you hear that noise. Most likely it is coming from some inductor. This relates to AC frequency into two pumps. So, the fundamental frequency of a pump is N is the RPM and a lot of these pumps water pumps or fluid pumps they have pressure chambers. So, whatever number of pressure chamber cycles they have in each revolution. So, N times NC over 60 and for this guy LW is 10 log again a lot of these pumps are rated in horse powers. So, you do not have to do a lot of conversion plus KP and KP is again provided by manufacturer or if you do not have anything then it is 95 dB for centrifugal pumps 100, 105. So, this is for screw pumps and this is for reciprocating pumps. So, the point here is not to make you experts in pump, but if you see or experts in electric motors, but if you see what types of noise emitting sources are there you should be able to figure out after some exploration which type of a signal or peak is attributed to what specific sources that is all I am trying to explain. Then you have some fans which have obviously they will have rotating blades, but in front of the rotating blades there are stator blades fixed blades right stator blades. So, fans with fixed and moving blades and you have these even small electronic fans or even in compressor fans. So, if you have this kind of a thing then the fundamental frequency is nr times nf times n over 60 times gcf, nr is number of rotating blades, nf is number of fixed blades and gcf is greatest common factor greatest common factor greatest common factor of nr nr. Do you understand why this where this is coming from? So, again you can calculate the fundamental frequency of the noise generated by a fan with fixed and moving blades using this approach and then you find it is harmonics and higher second and third and fourth harmonics and so on and so forth. Another example, most of the moving systems have gears right and they can also generate noise on their own. So, ideally a gear profile is involute you assume that teeth are rigid perfectly rigid and in theory they should not generate any noise, but in reality they are manufacturing errors, there are gaps if there is a gap the gear will come and hit one teeth will come and hit the other teeth. So, it will generate an impulse force also these teeth bend in reality. So, all this generates noise imperfections in geometry. So, these gears generate two different broad categories of noise one is one has a frequency which we call meshing frequency. So, a meshing frequency is n is the number of teeth on a particular gear times n upper case n is number of teeth and lower case is rpm divided by 60. So, if you have two gears which are meeting they have one single meshing frequency the smaller gear will have same meshing frequency the larger gear and then the other one is tooth error tooth error frequency. So, n is your rpm of a gear and n upper case is number of teeth on the gear whose rpm is n. So, tooth error is that suppose you have two meeting gears and one particular tooth is broken or damaged then in every revolution it will come in generate its own signature. So, we call that f 1 e and that is essentially n over 60 hertz right. What happens if there are two teeth which are broken and they are next to each other will it be 2 n or if that in that case the other broken tooth has to be opposite at 180 degrees phase difference right here you will have two impacts in one revolution. So, it will not be just 2 n it will be a combination of different signals right. So, what we will do is next five six minutes we will do a example on gear then we will close and then Dr. Kalyanamadevi is here for evaluation. So, that will close the. So, we will do one very quick example. So, I have a gear train this is a good simple example, but pretty educational. So, I have four gears 1, 2, 3, 4 and the number of teeth on this guy are 40, 90, 44, and 86 and my n 1 is 3600 rpm. Now, when this gear train runs its generating some noise. So, I measure the noise signal I plot it on a graph sheet and I find that there are peaks at different frequencies. So, my peaks are at 14 hertz, 27 hertz, 1, 2, 2, 7 hertz, 2400 hertz, 2455 hertz. So, 4800 hertz. So, the question for the engineer in this case you is that given this gear train can I develop some sort of a hypothesis that how is this sound getting emitted what are the sources of this sound assuming this gear train is the only source of the noise in the room. So, some possible explanations. So, what we do is we start computing different frequencies. So, n 1 is 3600 rpm, n 2 equals n 3 is 3600 times 40 over 90 that gives me 1600 rpm, n 4 is 1600 times 44 over 86 that gives me 818.7 rpm. So, now, I have figured out r p m of different gears. So, now, I find different fundamental frequencies. So, 2 th error frequencies f 1 e is what n over 60 right. So, for gear 1 e is what n over 60. So, for gear 1 it is 60 hertz, for gear 1, for gear 2 and 3 it is 26.7 hertz and for gear 3 it is 13.6 hertz no gear 4. So, remember this similarly the fundamental tooth meshing frequency. So, that is f equals n times upper case n over 60. So, we find this for all 4 gears. So, gear 1 and gear 2 they are meshed with each other they are same frequency that is 3600 times 40 over 60 that gives me 2400 hertz right and gear 3 and 4 that gives that is if I do the calculations right it is 1226.7 does do these numbers tell you some story. So, tell me 2 th error frequency of 2 and 4 which one 2 th error frequency of gear 2 3 and 4 are giving the first second 14 and 27 hertz 2 3 and 4 tooth error is for 2 and 3 it is 26.7 and 4 is 13.6 yeah. So, you are saying and then what about others and this 2400 and 1 to 2 7 is directly. So, that is one hypothesis and then how what you do is you go back and then inspect those gears and see whether that your hypothesis is indeed correct or not and then you see whether another slightly different interpretation could be that 14 and 27 hertz is coming just from 1 gear where you would think that is another way to think about it and that is coming from gear 1 to 2. So, that is one hypothesis number 4 that is another because yeah 26.7 is also fairly close to 27. So, I understand where you are coming from, but a lot of times you would not have two teeth broken teeth you know on two gears you have a broken tooth tooth each. So, that is another hypothesis. So, the point is that you have all these different types of approaches to figure out signatures of different moving components. So, similarly there are rules and formulae for ball bearings, chains, sprockets, belts, pulleys all sorts of moving components. So, you figure out what are the fundamental noise signatures from different components. Look at your fundamental overall noise spectrum and then try to intelligently start mapping what is coming from here also some of them may not be attributable to any of these moving components. So, in that case you may also want to see that am I exciting some structural member let us say you have a wide flat sheet metallic sheet and it gets excited at 55 hertz and that is showing up. So, in that so first develop a overall map of what type of frequencies are being generated by different moving components figure out can you map some of those to your noise spectrum. Second then start turning of each of these and see if you turn of one particular unit what happens there if it does not change anything then it is not coming from there. So, it is a very iterative process and here the understanding of the physical system is probably much more important than the understanding of noise itself. So, with this we come to a close. So, continuing on from what we had started in the last lecture today in the final lecture what we will cover is a little bit about active noise cancellation approach and the limitations of that approach. And then a very broad overview of how noise is controlled in different types of environments. So, active noise cancellation and a very broad overview of noise control in different environments cars machine shops and all sorts of places where we encounter noise. So, we start with active noise cancellation and the principle for the active noise cancellation is fairly straight forward and it may appear simplistic if I say that if you have a source which is generating noise then if I generate quote unquote anti noise signal then it gets cancelled and there is no noise. But this is a very simplistic way of approaching this because there are lots of ifs and buts and constraints when we try to cancel noise. So, that is what we will try to uncover in next 15-20 minutes. So, one approach noise could be cancelled is we will show here. So, let us call this approach one and in this approach let us say I have a room there is a listener here and let us say noise is coming from a concentrated source. So, I am getting a noise signal and it is not coming from all sides it is coming from a local area. So, to cancel this noise what I do is I place a microphone near this noise source send the signals to a box which could be a combination of a signal analyzer and signal processor well I mean. So, signal analyzer and corrector. So, it also generates correction signals and then it also amplifies to the appropriate level for every frequency and then that signal is then fed back to a transducer. So, it comes back to a transducer. So, that is my transducer. So, I have this noise signal coming and it is getting compensated by the corrector signal coming from the transducer and these signals reach the human ear and arguably and we will see limitations on this approach the human ear does not perceive any noise. So, now we will explore this a little more deeper at a conceptual level and try to expose some of the fundamental limitations of this type of an approach. So, the first limitation of this approach limitation 1 it relates to the time delay. So, in this the limitation is caused by time delay what do I mean by time delay by the time noise reaches this point and it is sensed by a microphone then the microphone has its own inertia. So, it takes some time to sense that noise then that noise is sent to this black box signal analyzer plus corrector plus amplifier and the electronics takes some time to develop corrective signals and that corrective signal then comes back and it is fed to a transducer. So, there is a delta t in this whole process also the location of the transducer is not identical to the location of the noise source. So, because of that separation physical separation of distance also there is a phase lag. So, the corrector signal reaches the human ear may be delta t seconds later than the original signal. So, that has implications in terms of what does that mean in terms of how much noise really gets cancelled. So, the time delay could be due to as we said microphone inertia it could be also due to electronics it could also be due to physical distance between this concentrated noise source we are not talking about a diffuse noise source we are talking that it is coming from a very local point kind of a source between source of noise and transducer which is emitting the corrective signals. Sir, how is a transducer cancelling them? How is a transducer cancelling the noise? So, in theory if I have a sine wave coming out as a noise then if transducer generates a negative sine wave whose amplitude which has a phase difference of pi. But it again depends where the person is because they will be since physical separation is there and the direction is also there. Yes. So, then the distance travelled by the wave from the transducer. So, that is what we are quantifying in this discussion. So, this cancellation will not be 100 percent and then that is what we are trying to sensitize you all that there is a limitation there will be some cancellation for some frequency wavelengths, but it will not be a broadband 100 percent cancellation. So, let us say because of this time delay let us assume a fairly small number of value of time delay. So, let us say this time delay is delta t equals 10th of a millisecond that is 10 to the power of minus 4 seconds and let us assume that noise is a pure tone and it is a cosine omega t and let us say that my anti noise signal if I do everything all the mathematics and electronics correctly that signal is a cosine what will it be omega t plus delta t times omega. So, if I expand this what I get is a cosine omega t times cosine omega dot delta t plus sine omega t times sine omega times delta t. So, at a mathematical level minus I have put outside oh yeah this has to be minus. So, at a mathematical level forget about the implementation even at a very mathematical and the level of principle the cancellation will be identical and 100 percent when this number is exactly 0 or it will be satisfactory when this number is fairly small and also this number is fairly small both of these numbers have to be small. So, let us look at some actual numbers. So, we assume that delta t equals 10 to the power of minus 4 seconds and we evaluate for different frequencies what are the cosine omega delta t and sine omega delta t terms. So, I am putting frequency in hertz 50, 100, 200, 400, 800 let us also put 1600. So, omega dot delta t and this is computed in radians, but if I transform to degrees in degrees my value is 1.8, 3.6, 7.2, 14.4, 28.8 and 57.6 in degrees. So, as frequency goes up very rapidly my theta is increasing and when you look at cosine values. So, this is approximately equal to 1, this is again approximately equal to 1.992, 0.969, 0.876 and this is 0.536 and the sine value is 0.031, 0.063, 0.125, 0.249, 0.482, 0.844. What you see is that may be just looking at some broad numbers may be this approach will work up to 100 or may be 200 degrees 200 hertz above that things become the sine value starts becoming fairly appreciable, starts becoming fairly appreciable. Also to give you a perspective delta t, if all the delay is caused just by the physical separation and the electronic delay is 0 which is not true, then delta t at 10 to the power of minus 4 seconds it corresponds to distance of what 0.0345 meters that is 3.45 centimeters. So, things have to be very close to the noise source and we are also assumed that the noise source is more or less a point source. So, there is a fundamental limitation in this approach. So, it does not work for high frequencies. The good thing about it that if it works when the person moves from one place to other place he will still have the same amount of attenuation noise cancellation because it does not depend on the location of the person, but the cancelling unit has to be fairly close to the source and the overall time delay has to be fairly small. But one thing can be done is that from the formula if omega delta t is 2 n pi. So, then even if there is time delay the it will be exactly exact noise cancellation. So, what you are thinking is that all the noise is purely sinusoidal. For this case I am saying. For this case but in reality noise is noise. So, it is essentially a very transient signal. So, if you have induced the delta t of 2 pi then it will be totally off in real noise conditions. So, that is there. So, again. So, first limitation we said is that so we will just write some limitations. So, it requires ultra fast processing does not work for high frequencies and the correction signal or sound actually not the electronic signal the actual sound has to be located very close to point source. So, this approach may work where let us say you have a generator which is running at a constant speed at fairly low frequencies 40 hertz 50 hertz 60 hertz 80 hertz. So, and then the person is fairly far away from that. So, then if you place a transducer and correct it you may have a very good performance. But if the source generates a broadband noise then high frequencies will not get attenuated and also if the source is distributed for instance if you are moving in a train all the walls of the train or if you are in a plane noise does not come from just one source. So, this approach has limitations in that sense. So, then the other extreme other extreme approach. So, here you have in this approach the transducer is very close to the source the other approaches you put the transducer very close to the here that is of the approach. So, we will talk about that also. So, you have the person and the noise is coming like this let us say this is his chamber through which noise is going in and hitting his place a transducer here and also if a microphone can be placed here. Then it does not matter whether the noise from which point the noise is coming from the noise is being sensed fairly close to the ear and the corrective sound is also being generated fairly close to the ear. So, because of this kind of an approach can handle sources of noise which are distributed in nature, but even in this case that you do not get away from the fundamental paradigm that delta t still has to be very small because of all the reasons which we talked about. It has to be very close to I mean because at very high frequencies or at high frequencies the requirement of delta t becomes extremely important. So, this approach also does not work well enough at high frequencies, but most of the attenuation at higher frequencies happens fairly well with passive approaches like you have a damping material on the headsets that those materials damp out high frequency, but this approach also works fairly well for low frequency content. The biggest issue with this is that you have to wear this device as you move. So, which is not a very appealing approach. A third approach is something like this. So, approach 3 is such that there is a room near the individual here sitting here and let us say a noise is coming from all directions right. So, again the noise is distributed. If this person is sitting at a fixed location then I can place a transducer here and this transducer generates the corrector signal and how does it generate corrector signal to understand that first you measure the transfer function H s between 0.1 and 0.2. So, between 0.1 and 0.2 we measure the transfer function. What that physically means is that the transfer function means is that if I generate a particular sound profile at 0.1 what will be its frequency spectrum at 0.2 right that is what transfer function is all about. So, based on that understanding and also if I. So, once I have this H s which is a fairly easy thing to do you generate a broadband noise source here you measure it here and then you take the ratios at every frequency you have your phase and magnitude plots for this transfer function. Once you have that then if you know what noise is coming at location 1 then you can compute what noise is being heard at location 2 right and from the same principles you can also figure out what kind of noise or what kind of corrective sound has to be generated at location 1 which will compensate that noise at location 2. So, using such a thought process you can develop a system which helps attenuate distributed source. How do you measure H s? How do you measure H s? That is fairly straight forward let us say you. So, we before applying the process we first calibrated. Yes. So, you have to initially you have to place a microphone at this location. And then calibrated. And calibrated right you have to place a microphone calibrated. In this approach also the requirements of delta t do not go away that is a fundamental. So, this approach also does not work for high frequency that is one. Second if this guy moves to a different location if the person is moves to a different location then you need to have a new transfer function. So, the validity of this approach is to the extent that the person is fixed in the room. A good example could be that if you want to attenuate sound noise levels in a car which is moving and let us say that noise is coming from the engine then because the person is fixed in a seat more or less then you can use this kind of an approach to cancel that voice. Another limitation of this is that because this distance is large because this distance is large and there may be sound sources which are fairly close to the human ear. By the time this character signal reaches even for low frequency content if there are some noise there is some noise content even at low frequencies which reaches the human ear significantly before the character signal comes then he has already heard it. So, that is another limitation. Then this will add up to the noise. Then it adds up to the noise. At a very basic level it is very people say oh you just generate anti noise and it will get cancelled but it is a very complex technical problem and there are physical limitations in what can be done and what cannot be done governed by laws of physics. So, with that overview of some basic strategies how noise is cancelled we will move to noise control. So, my aim is to minimize the noise a human being is hearing and to do that I have to understand how noise is getting generated how it is getting propagated from the source to the listener and how it is being interpreted. So, once I have understanding of all these three things then I can figure out how to control and regulate noise. So, at a very conceptual level you have a source and I have a listener. Some of the noise reaches this individual directly. So, this source just emits noise and atmosphere and it radiates and reaches the human person. In other cases the source is also vibrating and these vibrations get transferred to other structural members of the system. For instance you have an engine which generates vibrations because of that the transmission and the car vibrates and that generates its own noise. So, structural coupling and two structures are coupled one is not generating a lot of noise in decibel levels, but it is generating sufficient amount of vibrations to excite resonances in some other physically coupled structure. So, this guy goes into resonance and this emits sound and that sound reaches the human ear. So, structure to ear through ear. So, that is the other path and the third path is that I have airborne sound which excites some other structural member. So, here the coupling is what acoustic coupling is acoustic coupling and then from here some particular modes and resonances get excited. So, again sound reaches the person. Sir, what is structural coupling? Structural coupling is that pieces are physically connected. So, you have an engine let us say its first resonance happens at may be 5000 hertz, but it generates some low level of frequency content at 200 hertz and it is coupled to a big sheet metal structure whose resonance is at 200 hertz or may be 50 hertz. So, it gets excited that is a structural coupling. So, to control noise you not only require a good understanding of principles of acoustics, but more than that you have to understand what the nitty-gritty and details of the physical system which you are trying to monitor. That is more important than just understanding physics of sound because what you will not understand by just understanding the physical principles is what are the different signatures of different types of noise and frequencies which are getting emitted by different components. So, once that understanding is there then in a very broad sense some control strategies you can develop. So, first one is that we control the source and control I am not talking in the sense of control theory just. So, you can do this by better design if the product is being developed at the designs you are at a design stage. So, better design better selection of components and better maintenance this is extremely important maintenance and monitoring. So, this is how you control the source. The second thing is this airborne element this one. So, that to address that you do minimize airborne transmission and here we have to understand the acoustics of the work place requires acoustics of work place requires better requires understanding of understanding of acoustics of the work place. So, whether I have resonance modes in the room reverb times and all the discussion which we talked about. What can you do about this one? So, this is structural coupling how do you address this? Sir, does it need to come under the controlling the source? No, controlling source is basically I have an engine which is vibrating a lot if I can balance it for better and so it generates less vibrations. But let us say it is still generating at 80 dB 50 hertz vibration signal and that gets coupled to a sheet metal let us say roof of the car. So, then the roof of the car starts getting excited because its resonance it is at 50 hertz. So, on the structural coupling side you have to do basically structural design model analysis isolation it does not have to be necessarily physical isolation but isolation in the sense that sound does not and vibrations do not propagate easily isolation damping and so on and so forth. And the final one is active noise cancellation. So, people start with active noise cancellation but this is in general the most costly and probably the least effective approach in general. But if you already have a problem and then it is definitely looking at active noise cancellation but if things are being designed they are in getting you know people are planning then all these considerations could be kept in mind while the whole system is getting developed. So, at for each of these and actually most important in for this source we have to understand what kind of signatures different types of sources generate. For instance if I have a shaft which is rotating at 60 hertz and it has a little bit of eccentricity. So, instead of rotating just on axis it will do this it will wobble a little bit. So, we have to understand what will be the frequency of sound it will generate. So, obviously it will generate 60 hertz because it is rotating at 60 hertz and it is wobbling. So, for different moving components it is good to have a broad based understanding what kind of signals different types of components generate. Because then when you look at the overall noise spectrum which the ear is listening or the microphone is capturing then you say oh I see 100 hertz peak and this whole machine D is having this particular component which could generate a 100 hertz signal. So, then I correlate that peak to that particular component and then I explore it further and try to figure it out. So, what we will do today in the remaining lecture is just expose you to few different types of machines and see what kind of noise signatures they emit. So, we will start on that the other thing is that. So, that understanding the noise signatures of different components moving components is one thing. The other thing is getting some very coarse not accurate to second place or even first place of very coarse understanding of what is the total sound power level these different types of components are generating. So, that is another understanding we have to have. So, we will start talking about noise source power level you can call it P and this is in watts. So, this is that this particular relation P equals f n dot P m this is an empirical relation. So, I am not going to offer any proof or anything like that where f n is a factor conversion factor and P m is the actual power of that particular machine in watts. So, in the hand out which which you have if you look at table 14.1 what you have is different conversion factors for broad types of some machinery. For instance compressors you have 1 to 100 horsepower and if it is a low power compressor then it is 3 times 10 to the power of minus 7 and so on and so forth. So, there are standard some of these data are there you can extract the data and get some broad coarse understanding of what is the noise source power level generated by a particular type of machinery you can figure out from that. So, this is dependent on the power how much power they are transmitting which is basically torque times omega.