Transcript for:
Sound Wave Parameters Overview

hi learners it's em from sano nerds today's video is going to be on unit 3 the seven parameters of sound all sound waves including ultrasound have certain characteristics that have measurable quantities these measurable characteristics are called parameters and define the sound wave from which they are obtained there are seven parameters of sound waves that you will need to know frequency period propagation speed wavelength amplitude power and intensity now as we're learning these seven parameters i want you to keep five things in mind definitions including synonyms units symbols formulas and relationships and the sonographer impact you're also going to see a lot of sinusoidal graphs being used in this chapter to visually represent some of these parameters the graphs will look very similar to one another so you need to pay attention to the labeled units let's go ahead and get started with section 3.1 period and frequency period and frequency are closely related do you remember their special relationship to one another they are reciprocals and that means when period and frequency are multiplied together they equal one both period and frequency are defined partially though by the concept of a cycle a cycle or wavelength is one complete oscillation if we could follow one tiny little particle we would see the particles starting at resting moving to compression back through resting down to rarefaction and then back to resting and that would complete the cycle so it's resting through a whole compression through a whole rare fraction and back to its starting point on a graph for ease we typically go from baseline to a peak through the baseline down to a trough and back to the baseline this image shows three cycles and we can see one two three where this image shows 10 cycles so now that you know what a cycle looks like let's start focusing in on our parameters the first one we're going to learn about is periods now the definition of the period is the time it takes to complete one cycle so period is the time that it takes to make a cycle another way to think about it is the time it takes for an entire event for example the earth rotates on an axis and for the earth to rotate all the way around once we call that a day so the period of earth's rotation is one day 24 hours or 1 365th of a year now the units that we use for a period in ultrasound typically are microseconds but in reality it can be any unit of time now we use microseconds to express period because it is complementary to the frequency unit of megahertz and the average ultrasound value for period is between 0.06 to 0.5 microseconds when we see period used in a formula is typically going to be represented as the letter t for time and the one major formula that we'll see period used in is the reciprocal formula for frequency and period so we have time or period in microseconds is equal to one divided by a frequency in megahertz so from that formula we can see that period and frequency are inversely related and because they multiply to equal one they have that special reciprocal relationship we can say that if period gets longer frequencies get lower if the period gets shorter then we see that the frequencies get higher as far as your role in regards to period there isn't a whole lot that you can do period is determined by the machine and it cannot be changed by the stenographer period really is kind of innate to the transducer and the frequency chosen so there's not a knob on the machine labeled period that we can just turn and adjust the period as we'll learn in later units though the period does impact some other imaging considerations so we do want to understand that again period is the time for one cycle period answers the question how long does it take for one cycle to occur and we can say it takes one second one microsecond five seconds any unit of time for one cycle there are six cycles represented in this graph labeled at 1.8 microseconds the period of each cycle is 0.3 microseconds to calculate that base off of this image all we needed to do was count the cycles and then divide the time frame by the number of cycles so we can see that each cycle gets 0.3 microseconds because we took again the time frame divided it by the number of cycles that we can see and calculate our period the next parameter we're going to talk about is frequency now frequency and period are very very closely related so let's learn about frequency and then take a look at how they impact one another so the definition of frequency is that it is the number of cycles per second and i do have in parenthesis there or millisecond or microsecond it has to be a derivative of a second and i'm going to show you why in a little bit here frequency in general though is how often an event occurs and we usually express it in some sort of event per time length for example beats per minute that's how fast your heart rating that's the frequency of your heart beating is beats per minute once per day twice per day that's a frequency the frequency of filing taxes is usually once per year for many people but in regards to ultrasound and waves frequency is the number of cycles per second now in ultrasound we use multiple derivatives of hertz to label frequency now hertz in itself means one second but we can also use kilohertz and we can use megahertz and that's because there's a lot of types of frequencies that are actually related to ultrasound we might use hertz to describe the frame rate of the machine we might use kilohertz to describe the doppler shift frequency but we usually use megahertz to describe the frequency of the sound beam created by a transducer in ultrasound the average values range typically from about 2 megahertz to 15 megahertz but it's not uncommon to go as low as 1 megahertz or up to 17 megahertz in our formulas we are going to see frequency described as a lowercase f and here are the two major formulas that we're going to learn about frequency in this unit now there are tons of formulas that are going to relate back to frequency so make sure if you're going to try to organize them on your formula sheet you're leaving a lot of space for frequency so the two major formulas that we have include frequency being equal to one divided by time again that shows their reciprocal relationship and then we also have frequency in megahertz being equal to the speed of sound divided by wavelength by looking at these formulas we can see then that frequency and period are reciprocals and we've already discussed that if frequency gets higher periods get shorter if frequency gets lower periods get longer but new to us is now that frequency and wavelength are inversely related because wavelength is below the division bar we know that it is inversely related to the quotient so if frequencies get higher wavelengths are going to get shorter we're seeing an increase in the value of frequency we will see a decrease in the value of wavelength if frequency gets lower then wavelengths get longer and similar to period there isn't a whole lot the stenographer can do to impact frequency frequency is again determined by the machine in the transducer and can't be adjusted by the stenographer but we are actually going to cover a little caveat on this in a minute the biggest part for frequency and the stenographer is that the sonographer should always choose the appropriate frequency for the exam that they're performing i want to talk a little bit more about using hertz as a unit for frequency now hertz means events per second and it's okay to use derivatives of hertz to express frequency because one hertz is one cycle per second one kilohertz is one thousand cycles per second and one megahertz is one million cycles per second so we can convert numbers to easily come back to that events per second as we are looking at graphical representations of waves i really want you to pay attention to the unit that the lines are labeled in for example if this frequency was labeled at a time frame of one second this would be a 10 hertz wave if it was labeled at one millisecond it would be a 10 kilohertz wave and if it was one microsecond it would be 10 megahertz it would be incredibly hard to draw out an actual true 10 megahertz frame in a label of one second so we like to change the representation by changing the labeled time frame did you know that you cannot hear all sounds that is because there is a range of frequencies that are audible to the human ear including frequencies from 20 hertz to 20 kilohertz but then we also have frequencies that are too low to hear which is infrasound and at less than 20 hertz frequency and there are frequencies that are too high to hear which is ultrasound or more than 20 kilohertz now we say that ultrasound is anything more than 20 kilohertz because it's ultra or above the audible range but remember in diagnostic clinical imaging the range is typically 1 to 17 megahertz so we have ranges from very very low frequencies to very very high frequencies low frequencies usually come with a lower pitch so they are very low where high frequencies come with a really high pitch now what's interesting about human hearing is that we do have this range again 20 hertz to 20 kilohertz is the audible range for humans but as we get older we actually get worse at hearing and what ends up going first is the ability to hear high frequencies so when you are you know four or five years old you might be able to hear all the way up to 20 kilohertz but after you've been to enough concerts or around enough machinery you might only be able to hear up to like 11 000 kilohertz so it's actually really kind of interesting and i have a video here if you've done this before please feel free to skip over this part it's about a two minute video but i just kind of wanted to show you what it sounds like when we are going through the audible range of sound i will say if you are on headphones right now you might want to turn down your volume or take your headphones off because it does get a little intense when we get into higher frequencies and then pay attention to when you can start to hear it and when you can not hear it anymore i'm just able to start to hear it now if you can hear it too you'll hear that's a really low pitch it's a low frequency so the frequency is continually increasing we're getting into a higher pitch higher frequency the periods are getting shorter so we're about halfway through the audible range of humans i just lost it at about 14 000. i assure you if you are still listening you might still be able to hear it and that was it so we went all the way from 20 hertz to 20 kilohertz the audible range of humans and again anything lower frequency than 20 hertz we cannot hear it because it's infrasound anything above 20 kilohertz or 20 000 hertz is considered ultrasound because it's above the audible sound i mentioned when we were originally talking through the frequency chart that we cannot adjust frequency and if you've looked at a machine yet you've probably seen a button on there that might say something like multihurts or you may have been told by another sonographer to adjust your frequency and so now you're thinking i'm a liar well here's the deal no we cannot change frequencies so if you ever get asked that on a test make sure you say no older machines used to have transducers with what we call limited bandwidth so if you wanted a low frequency transducer for an image then you had to pull out the transducer that had the two megahertz four megahertz frequency but if for some reason you were adjusting and wanted a high frequency transducer then you had to go get a whole brand new transducer and plug that one in and switch to it so older machines the only way you could change frequency was literally by getting a new transducer there wasn't anything you could really manipulate to change the frequency and that's still kind of true today but what we see with modern transducers is that they have a little bit larger bandwidth so i have an image here of three transducers the first one is called the hockey stick it has a frequency i believe up to like about 17 megahertz but the other two that you can see have little numbers written on the side so the middle one is a linear 12 5 transducer and the one on the right is a curve linear 5 1 transducer and those 12 5 and 5 1 are the bandwidth or the frequencies that the transducer is capable of producing and we're going to learn how the transducer creates frequencies and creates a sound beam but essentially what happens is that this little chirp comes out of the transducer and within that chirp are a bunch of different frequencies from 12 megahertz to 5 megahertz and five megahertz one megahertz depending on the transducer that you're using as a sonographer knowing how frequency affects your picture what you can tell the machine to do is listen for a certain frequency so if you have a multi hertz button and you change it you can change it to say only listen for the 12 megahertz echoes or only listen for the five mega hertz echoes i need more penetration from my picture so in reality no we are not changing the actual frequency that is innate to the transducer but rather changing some modern machine parameters in which we can change which frequency we are listening for so why do we have different frequency transducers we're going to learn a lot about frequency throughout the book but one of the biggest roles as a sonographer is for you to understand why you're making the choices you make based on ultrasound physics and frequency is really a big one we must balance what we want for detail resolution with the need for creating diagnostic images now a transducer with a capability of 12 megahertz to 5 megahertz is going to be very very good at showing detailed images of anatomy that's a relatively high frequency at that 12 megahertz but the problem with high frequencies is that they don't image very deep into the body because they attenuate very quickly so a 12 to 5 megahertz transducer is going to be perfect for imaging structures in the neck but it's not going to give you anything more than like a skin line or some muscles if you're trying to use it on somebody's stomach so that is where we compare that then to a frequency range of say the curve linear which had a five to one megahertz range now that one megahertz range is going to be awesome for penetrating into the body it can image like 20 centimeters in but the detail is not going to be as prevalent so as a sonographer you really are trying to balance the best frequency for the exam that you are performing balancing detail and creating a diagnostic image i think we would all agree that being able to see anatomy and maybe a little bit poorer detail is much better than not seeing it at all but sometimes you're not making that extreme of a decision maybe it's a difference of a couple megahertz and the difference between seeing small structures well and kind of getting a little bit blurrier so just like period answered the question how long does a cycle occur frequency answers the question how many cycles can occur in one second or millisecond or microsecond so in this image here we have one cycle the frequency of this is one hertz because it is one cycle occurring in one second or it would be one kilohertz because it's one cycle occurring in one millisecond or we could say it's one megahertz because it's one cycle occurring in one microsecond again we're using those complementary prefixes here again we have six cycles represented in this graph labeled at one second and the frequency is six cycles per second or six hertz to calculate that based off of this picture all we need to do is count the cycles so again we have six cycles divide that by one second and because frequency and hertz are defined as cycles per second or events per second we can say that this is a six hertz frequency but we need to be really careful about our labels look at this one we've got it labeled at two seconds we have six cycles but now it's six cycles per two seconds and frequency and hertz are per one second so we do need to reduce that down and we end up getting three cycles per one second which gives us a three hertz frequency and just to reiterate a concept that i've talked about already we can figure out the frequency easily and really make it more applicable to ultrasound if the graph is represented in milliseconds or even microseconds so for example this graph is labeled as one millisecond when the graph is labeled in milliseconds we are know that we are seeing a frequency represented in kilohertz this graph has six cycles so we can say that we have six cycles per one millisecond we can convert that then to six thousand cycles per one second which is the same as six thousand hertz or converted to six kilohertz same idea with microsecond again we have six cycles per one microsecond we convert that up to six million cycles per one second and that is the same as saying six million hertz or 6 megahertz so here comes back all of that metric staircase stuff this is why you need to be able to convert easily between base units and prefixes so let's review how period and frequency are related to one another again period and frequency are reciprocals because if you multiply frequency by the period they should equal one based on that formula we can manipulate it to solve for frequency and solve for period now remember this formula is more applicable to ultrasound because we're talking about frequencies in megahertz and periods in microseconds you can change this formula to reflect the units that you're working in so here i've changed it to more base units where period is in seconds and frequency is in hertz so let's try an example if we are showing a graph like this we can count the number of cycles that occurred so we have two cycles per one second and that lets us calculate that the frequency of this graph is two hertz we then know that we can just take the reciprocal of two and figure out the period so one divided by 2 is 0.5 so if we calculate frequency first by counting the cycles and making that into hertz we can calculate period by making a reciprocal of it on the flip side of that though we have a time frame so we can also figure out period first so we take the time frame and divide it by the number of cycles that gives us 0.5 seconds or half a second again because period and frequency are reciprocals we can take the reciprocal of 0.5 to calculate the frequency which is 2 hertz so i encourage you to work with both ways of calculating these but stick to the one that makes the most sense to you there's no point in making this harder on yourself because i want this concept to really solidify in your brain we're going to head over to the board to try out a couple examples if you feel like you understand it feel free to skip this part and join us back for the discussion let's just do a couple more examples using period and frequency to figure out one another so here's our example we have three cycles on this waveform we have one two and three let's go ahead and give this line some sort of time frame let's say that this is one second we're going to start out easy so we have one second three cycles so we can easily figure out the frequency by counting the cycles and applying the second to it so we have three cycles per second and because we're already in the cycles per second we know that's hertz so we can say that this is three hertz now to calculate the period all we need to do is change three hertz into a reciprocal and that will be the period so to do that we take three and move it into the denominator spot under a one so one third of a second equals the period which is also 0.33 repeating what if we change the time frame though let's say now our time frame is over six seconds so we have three cycles per six seconds and we can't just say that that is three hertz because it's not a cycle per one second so we need to change that six seconds back to a one so to do that we need to divide six by six we'll get one a second but if we divide six by six then we also have to divide the three cycles by six and when we do that we get half a cycle so now we have 0.5 cycles per one second which means we have a 0.5 hertz for frequency to figure out period then we just need to take the reciprocal of 0.5 so we would do 1 divided by 0.5 which equals 2 for our period so this wave at 6 seconds has half a hertz for a frequency and a two second period so hopefully you're starting to see that really all we need to do is count the cycles figure out hertz or figure out frequency and then take the reciprocal of it to find the parameter that you didn't originally calculate let's do one more example but looking at more of an ultrasound value this time we have a graph showing us 10 cycles and we're going to say that this is occurring over 1 microsecond so 10 cycles per 1 microsecond gives us automatically a frequency of 10 million hertz or 10 megahertz because we're matching megahertz with the microsecond if you want to see the math on that we would take one microsecond and convert that to one second to do so we take one microsecond and multiply it by a million so multiplying by one million on the bottom gives us one second if we multiply on the bottom then we got to multiply on the top by 1 million so multiplying 1 million by 10 gives us 10 million cycles and 10 million cycles per 1 second equals 10 million hertz which is the same as 10 megahertz so that's why we know when we have a time period of one microsecond whatever we're seeing for our waveform is automatically a megahertz frequency but regardless we can take our 10 megahertz and we can take the reciprocal of that so 1 over 10 and that is going to equal 0.1 microseconds again we want to use complementary units so this wave has a 10 megahertz frequency and a 0.1 microsecond period all right welcome back go ahead and pause the video and start working on your period and frequency practice in your workbook you are going to be presented with a chart where one of the pairs are missing so you'll be missing either period or frequency and your job is to fill in the chart make sure that you're using complementary units and then as a bonus practice you can decide if the frequencies that you calculated or that are already there are audible infrasound or ultrasound go ahead and unpause the video when you are ready and here are the answers to the period and frequency practice remember that we want to use the same units so seconds and hertz need to go together microseconds and megahertz milliseconds and kilohertz and then if you went through and also figured out if these are audible infrasound or ultrasound here are the answers to that now that last one in the bottom corner 0.25 kilohertz may have been a little tricky you may have initially wanted to say that that was in for sound but remember that audible sound ranges from 20 hertz up to 20 kilohertz and 0.25 kilohertz is actually 250 hertz so it is in the audible range next up we have section 3.2 wavelength and propagation speed now section 3.1 just told us that period and frequency are reciprocals that both period and frequency are controlled by the machine and transducer and neither period or frequency can be adjusted by the sonographer in this section we are going to see how wavelength and propagation speed share some similarities and then put all four parameters in relation to one another at the end go ahead and start with propagation speed the definition of propagation speed is the speed that a sound wave travels through a medium remember those rules that we talked about those five things you have to know about sound sound has to travel through a medium and how fast it travels through that medium is called propagation speed so propagation speed is the rate at which a sound wave will travel through a medium now the only way speed changes is if the medium changes all frequencies will travel at the same speed through any given medium so if you have a one megahertz transducer on the body it's going to travel at the same speed as a 17 megahertz transducer as far as units for propagation speed go we use meters per second and millimeters per microsecond now in ultrasound the body is made up of several types of mediums and since we don't know what medium the sound wave is encountering at any one moment what we've come up with is a soft tissue average and that soft tissue average is 1540 meters per second or 1.54 millimeters per microsecond now the symbol for propagation speed might seem a little off but it is symbolized as the letter c so you will see the letter c in your formulas what this is basically showing us is what the relationships are and those relationships are very important for understanding propagation speed so the first relationship that we need to know is that speed and stiffness are directly related when a medium is stiffer the speed is going to be faster through it if a medium is more elastic then the speed becomes slower the formula also shows us then that speed and density are inversely related if a medium is more dense we find that the speed is slower if a medium is less dense then the speed is faster now the stenographer has very little impact on propagation speed and that is because propagation speed is only determined by the medium we can't adjust it but we do need to know what the average soft tissue speed is 15 40 meters per second and we need to know the basic speeds and other types of mediums period answered the question how much time does the cycle need frequency said how many cycles can occur in one second propagation speed answers how fast sound travels through a medium and here we have a chart of some really common mediums along with their propagation speed now some of these numbers might vary from other sources that you might have opportunity to see i did find that air water soft tissue and bone probably were the most consistent among the resources that i took a look at but the biggest thing that we can pull from this is that items that are not very sick like air like lungs have really slow speeds so low stiffness low speeds comparing that to bone which is very stiff having a higher speed we do need to memorize that soft tissue is the average of the tissue found in the body and you should be able to reason why air and lungs are the slowest where bone is the fastest and then kind of figure out how lungs fat and water on the slow side versus like liver blood muscle or on the higher side and i'm going to repeat it again because it's so important that we know this number ultrasound machines assume an average propagation speed of 1540 meters per second or 1.54 millimeters per microsecond in soft tissue now i've mentioned stiffness and density but what do those really mean well stiffness is a medium's ability to resist compression a synonym for stiffness is the term bulk modulus now bulk modulus and stiffness have the same meaning where elasticity and compressibility talk about the same characteristics but in an opposite way so for example a marshmallow a marshmallow has low stiffness and low bulk modulus but another way we can describe that marshmallow is having high elasticity and high compressibility so they are all referring to the same characteristic but go about it in different ways you need to be able to interchange these terms now as far as density goes density is the mass per of volume so when we have something that weighs a lot but takes up very little space that item is very dense compared to something that weighs very little and takes up a lot of space so for example if we have a pound of feathers and a pound of lead the pound of feathers is going to have low density because a pound of feathers is going to be a giant bag of feathers compared to just a very tiny cube probably of lead so the lead is very dense because it takes up a little amount of space where the feathers are not dense because they take up a lot of space for the same weight let's go ahead and switch over to wavelength then wavelength is the distance a cycle takes up in space now if we could get out a tiny little ruler and measure the sound wave from the start to the end of a cycle we would know the wavelength thankfully though wavelength period and frequency are all related so we actually have formulas to help us with those calculations we see that wavelength is represented in a unit of length typically millimeters and in clinical ultrasound we see that the average value of wavelength is usually about 0.1 to 0.8 millimeters in soft tissue and we're going to talk about why we define the medium soft tissue when we talk about wavelength in a minute here now the symbol for wavelength is the greek letter lambda which looks like a little upside down y and here are a couple formulas related to wavelength now on the top you will see that wavelength is equal to c if you recall c is propagation speed divided by frequency in megahertz and below that i have a very similar formula where it has lambda equal to 1.54 millimeters per microsecond divided by frequency in megahertz so we have a general wavelength formula on top where c can be represented by any propagation speed propagation speed of air of bone of anything where in soft tissue we can change the c to a constant number so let's look at the relationships then that these formulas represent please tell us that wavelength and frequency are inversely related so when wavelengths are longer it's because the frequency is lower if a wavelength is shorter then we see that the frequency is higher we also see then that wavelength is directly related to propagation speed so when wavelengths are longer it's because it's going very fast through a medium the propagation speed is higher when wavelengths are shorter it's usually because the speed has decreased as far as what you can do to wavelength as a sonographer again there isn't much and this is because wavelength is not only determined by the frequency which is a machine based parameter it's also determined by the body or the tissue the medium in which the sound is traveling through so we can't adjust either of those but we do need to know that shorter wavelengths are going to improve axial resolution so wavelength is going to answer the question how much space does a cycle take up again if we could get a ruler out and measure this how long would it be would it be one millimeter would it be one centimeter would it be 1.3789 meters it could be any unit of length so here we're back to our graphical representation we have six cycles represented in this length labeled at nine millimeters now to determine the wavelength based on this graph again we would want to count our cycles and then divide the length by the number of cycles and that gives us 1.5 millimeters per cycle so each of these cycles takes up one and a half millimeters of space now when we represented the graph as a length it was easy enough to calculate the wavelength just by counting the cycles and doing basic division let's take a look at what it means to apply frequency and propagation speed to calculate the wavelength first though we need to realize that frequency will affect the wavelength in a particular way remember that wavelength and frequency are inversely related so low frequencies have long wavelengths and high frequencies have short wavelengths the top wavelength is an eight megahertz frequency we have eight cycles being represented in the time frame of one microsecond the bottom is a three megahertz frequency we have three cycles being represented in one microsecond we can see that both waves are represented in the same time frame the one microsecond and you can see that the eight megahertz cycle length is much shorter than the three megahertz cycle length however we still don't have enough information though to calculate the wavelength of either of these frequencies and that is because wavelength is determined by the frequency and the medium it travels in so we need both pieces of information to calculate the wavelength so let's say we have these graphs again and this time we're going to say that they are traveling through air now the propagation speed of air is actually really slow at 330 meters per second or 0.33 millimeters per microsecond now if we use our knowledge that we have an eight megahertz and a three megahertz frequency plus the knowledge of our propagation speed we can use the general formula for wavelength we replace c with the propagation speed of air we replace f with our frequencies and calculate that the eight megahertz sound wave traveling in air has a wavelength of zero millimeters compare that then to the three megahertz wave traveling in air with a 0.11 millimeter wavelength again this is proving that high frequencies have short wavelengths compared to lower frequencies with longer wavelengths however we are in ultrasound physics so we are going to replace the c with our constant value of 1.54 millimeters per microsecond whenever you see the phrase traveling in soft tissue or some variation of it you need to automatically know that soft tissue speed is equal to 1.54 millimeters per microsecond and automatically replace that in your wavelength formula so again we have our eight megahertz and our three megahertz frequencies traveling through soft tissue we can plug our values in and we find that the eight megahertz wave has a 0.19 millimeter wavelength compared to the three megahertz wave which calculates to a 0.51 millimeter wavelength sometimes it's just very helpful to have some values off the top of your head and if you can memorize a couple values it might also jog your memory on what the formulas are as well so here are a couple easy ones to remember for one megahertz and two megahertz the one megahertz frequency has a period of one microsecond and a soft tissue length of 1.54 millimeters because it would be 1.54 divided by one and then simple enough from there you can look at the two megahertz frequency and see that it is a 0.5 microsecond period and a 0.77 millimeter wavelength again just knowing these off the top of your head might actually prove very beneficial for quizzes and tests to round out this portion of section 3.2 i do want to cover period frequency wavelength and propagation speed as they are all related to one another we know that if we have a picture of a graph and we know what the medium is we actually can calculate period frequency wavelength very easily from only having a little bit of information so we are going to head over to the board to talk about the next three pages in your workbook and kind of just show you visually how the math works out for all of these so if you understand the written description of the math you are welcome to skip the board presentation come on back for the discussion let's look at our first example in the workbook the workbook tells us that we have a waveform that looks like this with five cycles on it and it is occurring over the distance of 1.5 millimeters so we have five cycles within 1.5 millimeters the other big thing that we are told is that it is traveling in soft tissue and with this information now we can calculate propagation speed wavelength period and frequency just based off of this information so let's go ahead and do some math we are going to start with filling in our propagation speed we've been told it's in soft tissue so we are going to fill in 1.54 millimeters per microsecond next i'm going to try calculating wavelength because i've been given a distance for my five cycles that's going to be the easiest thing to calculate next i'm going to take my distance and divide it by the number of cycles that i have so 1.5 divided by 5 and that gives us 0.3 millimeters per cycle now i have the information of propagation speed and i have the information for my wavelength which means i can figure out frequency frequency then is going to be equal to propagation speed divided by the wavelength so 1.54 divided by 0.3 gives us 5 megahertz and now that i have my megahertz i can now calculate period by taking the five megahertz and converting it into reciprocal so we take the one and divide it by the five and that is going to give us 0.2 so our period is 0.2 microseconds and there you have it we have all of the math to show us the parameters that are represented by this graph let's go ahead and try the next example our next example again is five cycles shown in the graph this time though we are under a 10 second label so these five cycles are occurring over 10 seconds and again we're told that this is in soft tissue so let's go ahead and put in our soft tissue propagation speed now i'm not going to use the 1.54 millimeters because look at my time frame is in a base unit so i'm going to use the 15 40 meters per second so i can stay consistent with using base units now i need to figure out what i can figure out next i have a time frame of 10 seconds and i have five cycles it actually is going to be pretty easy to figure out period because i can take my time frame and divide it by the number of cycles i have 10 divided by 5 is 2 so my period is 2 seconds now that i know my period i can figure out my frequency by taking the reciprocal of 2 so 1 divided by 2 equals 0.5 or one half so we have 0.5 hertz because seconds and hertz match up so now we can figure out wavelength based on our wavelength formula but we got to be really careful what i've presented to you for the most part has been a wavelength formula using ultrasound applicable units this time let's write the wavelength formula using base units so we're going to have our wavelength in meters instead of millimeters being equal to 15 40 meters per second everything's matching up divided by our frequency in a base unit of hertz notice that all of our units are complementary to one another now we can take 1540 and divide it by 0.5 and we get 3080 and because we're in meters our wavelength for this wave is 3080 meters very important that you are converting units so that you are using similar units throughout or your calculations are going to be incorrect our last example changes the graph down to a three cycle waveform and changes the label to one microsecond now we have a couple ways that we can go about this we can count the cycles and divide it by the one microsecond or we can figure out period first by dividing one microsecond divided by three cycles so for this example we're going to figure out frequency first so we've already counted the cycles there's three of them and we see that it's under one microsecond so we have three cycles per one micro second and i've already explained that if we see one micro second we know automatically we are looking at a megahertz frequency so we are just going to jump to that conclusion now so we've got three megahertz as our frequency from here we can figure out the period easily by taking the three megahertz and taking its reciprocal so one divided by three megahertz is equal to 0.33 microseconds so our period is 0.33 microseconds and we know it's in soft tissue so we can go ahead and fill that in we're going to go back to our ultrasound relevant units here so now all we have left to figure out is the wave length and we can take 1.54 and divide that by 3 in megahertz and when we do that we get 0.51 so our wavelength is 0.51 millimeters so by knowing that frequency times period equals one and then being able to find the transpositions of those is going to be very helpful and then also knowing your wavelength in soft tissue are two formulas that are going to help you immensely so if there's two formulas that i would really focus on that i understood well it would be these two all right welcome back there's just a few things that i want to cover about those examples that we went over first off a lot of information can be derived from just one or two pieces of information if you know your formulas so make sure you know your formulas and practice them when we use a graphical image to describe a wave the parameters change drastically based on those labels so make sure you're always checking your axis labels units and formulas are also super important we would have had a very wrong answer for example too if we had left our frequency in hertz or didn't transpose the formulas to represent hertz instead of megahertz and now number four here's an example of what an actual question might look like so what is the wavelength of a three megahertz wave traveling in soft tissue now this was an example that we did earlier but looking at the answers here we have three millimeters three meters 0.5 millimeters and 0.05 kilometers and what this question is basically asking do you know what the speed of soft tissue is do you know the wavelength formula and can you calculate it if you can't get that off the top of your head you can start to look through the answers and do some process of elimination we would know that three meters is super big and way out of the normal range of ultrasound which three megahertz is in three millimeters is actually out of the range of ultrasound as well so that kind of eliminates that one and then if we convert 0.5 kilometers we get a very large number which is also out of the range so if you know nothing but your ranges you can also still answer this question so we're going to pause here and take a moment to work through another chart that's missing some information on this chart though you're going to be filling in the answers for very common frequencies used in ultrasound so they are all ultrasound based units come on back when you're ready to see the answers and here are your answers so everything in bold was given to you you needed to fill in the other spaces so note in the frequency column we started with one megahertz two three and a half five seven and a half ten and fifteen so we've increasing frequencies as we move down the columns we should therefore then see periods decreasing as we move down the columns and we should see wavelength values decreasing as we move down the column and propagation speed in the last column should be 1.54 millimeters per microsecond all the way down to recap 3.1 told us that period and frequency are reciprocals both period and frequency are controlled by the machine on the transducer and neither period or frequency can be adjusted by the sonographer section 3.2 just told us that wavelength is dependent on the machine and the medium propagation speed is dependent only on the medium and neither can be adjusted by the stenographer so what are the strength parameters well there are three more parameters to cover and they are going to describe the strength or the size or the bigness of the wave and they are going to include amplitude power and intensity now there are four things that you should know about the strength parameters first all three parameters are directly related to one another so if amplitude changes power intensity also change they're all related secondly all three parameters are determined by the machine so machine decides what the strength parameters are number three all three parameters can be adjusted by the sonographer and you do so by adjusting the machine's output power and lastly all three parameters even though they are determined by the machine they will start to weaken or attenuate as they propagate through the body so the body does have some acoustic propagation effects on these three parameters another thing you should know about this section is you're going to see this funny little symbol that looks like an open-ended infinity sign whenever you see this you should read it as is proportional to so let's start with our first strength parameter amplitude now the amplitude definition is the difference between the average value of an acoustic variable and its maximum or minimum and those are pressure changes density changes and distance changes technically decibels can also be used to describe amplitude because amplitude can refer to the loudness of a wave but we'll talk about that more in subsequent units now the reason that amplitude can be described in these three units is because they are the units of the acoustic variables remember pressure density and motion pressure is the most common ultrasound amplitude that we discuss and the common ultrasound values range from one to three million pascals or one to three megapascals the symbol for amplitude is a capital eight and here are a couple formulas that you might see it in first we have power is proportional to amplitude squared and then we have intensity is proportional to amplitude squared now these relationships will show us that if amplitude increases by a factor both power and intensity are going to increase by that factor squared and if amplitude decreases by a factor both power and intensity are going to decrease by that factor but squared as far as impact goes amplitude is determined by the output power of the machine but will weaken as it propagates the sonographer can adjust amplitude by adjusting the output power so amplitude is one of the ways that we describe the strength of a wave amplitude is measured by determining the change of an acoustic variable from its resting or neutral position when no sound wave is present to the max compression or the max refraction so amplitude is from the baseline to a peak or the baseline to a trough now there is another term called a peak to peak amplitude this measurement is rarely used but amplitude is considered to be half of the peak-to-peak amplitude the amplitude typically translates to loudness to human ears for audible sounds the strength of the wave and ultrasound though will affect the brightness of the echoes and bio effects so increased amplitude typically means louder or brighter echoes where decreased amplitudes mean quieter or darker echoes next up we have power the definition of power is the rate of work or energy transfer now light bulbs are really good way to help us to understand power when a light bulb has a higher wattage it's a brighter bulb so 100 watt bulb is much brighter compared to a 40 watt bulb this is because there's more energy being transferred into light energy which makes it brighter the units for power are milliwatts or watts and the power range can vary depending on how the stenographer has set the machine typically in ultrasound we see power ranging from 4 to 90 milliwatts the symbol for power is a capital p and putting in our formulas again we have power is proportional to amplitude squared and powered is proportional to intensity so again defining those relationships if amplitude increases by a factor power intensity both increase by that factor squared same for the opposite if it decreases by a factor we'll see a decrease in that factor squared new to this part though we have power is proportional to intensity so that means that if power increases by a factor intensity increases by the same factor and similar to amplitude power is determined by the output power of the machine but will weaken with propagation the sonographer can adjust power by adjusting the output power lastly then we have intensity and now the definition of intensity is the concentration of energy in the sound beam so the power put out by the machine does affect the intensity of the beam so does the area of the beam so in general if we have more power over less area we can make a really strong beam where less power over more area will cause the beam to be weaker think for example of the sun if you have the sun shining on a pile of dead leaves nothing much happens to them they we can just see them they're they're in the sun but if you take a magnifying glass and focus the sun into a very small area you can actually set the pile of leaves on fire so when we have energy spread out over a large area like the earth the intensity isn't very strong comparing that to taking the sun's energy focusing it into a very very small area the intensity becomes much stronger now the units of energy are watts per square centimeters and that is because it's related to watts power and square centimeters in area the symbol for intensity is a capital i and so we've already seen the intensity in its relationship to amplitude squared and power but a new one for us is intensity equals power over area so to look at the intensity formula we see that intensity is directly related to power and inversely related to area again power is above the division bar it's the numerator the numerator and the quotient are directly related where the denominator and the quotient are inversely related so if intensity gets stronger power gets stronger or area narrowed we can then say if intensity weakens that the power weekend or the area became wider and just like the other three strength parameters intensity is determined by the machine based on the output power it will weaken with propagation the sonographer can adjust intensity by adjusting the output power so let's review these three concepts power is proportional to the amplitude squared intensity is proportional to amplitude squared and power is proportional to intensity one of the ways in which we like to test you is is to see if you understand how when power increases what happens to amplitude what happens to intensity are you able to talk about those changes so when we are considering how values change in relation to one another we need to keep a few rules in mind first increasing by a factor means to multiply so increase by a factor of two means you're multiplying by two decreasing by a factor means to divide when you decrease by a factor of five it means to divide by five when amplitude increases by a factor power and intensity will increase by that factor squared now the same is opposite when amplitude decreases by a factor power and intensity will decrease by that factor squared and then i just want to go over a few common phrases that you might see in relationships to describing how things are related to one another so first off doubling something is the same as increasing by a factor of 2 or multiplying so if you say amplitude doubled that means that amplitude increased by a factor of 2. having something is the same as decreasing by a factor of two so if i say amplitude was halved that means it decreased by a factor of two quadruplin is the same as increasing by a factor of four or quartering is the same as decreasing by a factor of four another thought about decreasing by a factor is that we can actually phrase it in a different way as making something reduced by a fraction or it's a fraction as strong so for example if we say amplitude is halved that means to decrease by a factor of two and because power and intensity need to decrease by that factor squared we could say then that power and intensity decrease by a factor of four or we could say that power is a quarter as strong as it was decreasing by a factor can also be termed as reduced by a fraction so for example if we say that we are decreasing by a factor of 4 it's the same as saying reducing by 1 4. now these next charts are all in your workbook and we are going to head over to the board again to go over the math to calculate these so again if you look at the charts and they make sense to you please feel free to skip the visual math section of this and join us back for the discussion in this section's examples i gave you six different scenarios that we can take a look at based on original values and changing one of our original values by a factor let's go ahead and go through them our first one asks us if amplitude increases by a factor of 2 what happens to intensity and power so it is saying that amplitude is going to be multiplied by 2 or increased by a factor of 2. if amplitude increases by a factor of 2 then power and intensity need to increase by a factor of 2 squared so amplitude would be 1.2 times 2 equals 2.4 power would be 25 milliwatts times 2 squared or 4 and that would equal 100 and intensity would also be multiplied by a factor of 4 which equals 20. so once you can figure out what the factor change is for amplitude square it and apply it to intensity and power the next example asks us if amplitude decreases by a factor of two what happens to intensity and power well decreasing by a factor of two means to divide by two so if amplitude is being divided by two then power needs to be divided by 2 squared so does intensity so now we can do our math 1.2 divided by 2 equals 0.6 25 divided by 2 squared which is 4. equals 6.25 and intensity divided by 2 squared or 4 equals 1.25 if your amplitude is decreasing by a factor then we need to divide all the values our next scenario asks us what will happen if amplitude increases by a factor of 3 so now we are going to multiply amplitude by 3 and if we multiply amplitude by a factor of 3 then we are multiplying power and intensity by 3 squared so 1.2 times 3 equals 3.6 25 times 3 squared which is 9 is going to equal 225 and intensity multiplied by 3 squared which is also 9 is going to be 45 so this is where knowing how to square numbers easily is going to come in very handy for answering some of these questions the next example then asks us what happens if amplitude decreases by a factor of three so remember decreasing by a factor is to divide if we divide amplitude by a factor of 3 then we divide power and intensity by a factor of 3 squared which again is 9. so 1.2 divided by 3 equals 0.4 25 divided by 9 equals 2.78 and 5 divided by 9 equals 0.56 now our next two examples change which factors change it's pretty easy if we know the factor that amplitude has changed to apply that to intensity and power what happens though if we are given that intensity or power changes how do we figure out the rest so in our first example we have intensity increasing to a new value of 80. so to figure out how much intensity increased we're going to take 80 and divide it by 5. 80 divided by 5 is 16. intensity has increased by a factor of 16 it was multiplied by 16. whatever factor we increase intensity by we also need to increase power by so 25 times 16 equals 400 now here comes the tricky part we need to figure out what we increase amplitude by so there's something called a square root and you may have seen this symbol over a number at some point during your math studies but the square root basically means to find the number one multiplied by itself will equal the number in our case 16. so we are looking for a number that satisfies something like b times b equals 16. and again this comes back into either knowing your square roots or knowing what numbers square you can do this through trial and error you can go through them you know 2 2 squared is 4 3 squared is 9 4 squared is 16 and that's actually what our answer is going to be so if amplitude intensity increase by a factor of 16 then amplitude is increasing by a factor of 4. and we can check that if amplitude increases by a factor of 4 then intensity needed to increase by a factor of 4 squared as did power and in fact they did they increased by that 16. so all the math checks out we can finish this one up by multiplying 1.2 times four and we get 4.8 all right our last example under this one then tells us that power decreased to a new value of 1.56 so now we have to figure out how did 25 get to 1.56 well if we divide 25 by 1.56 that tells us that power decreased by a factor of 16. so now we divided 25 by 16 to get the new value of 1.56 and again using the rules that we've learned intensity also has to divide by 16 or decrease by a factor of 16 and we get 0.31 and just like we saw last time we need to figure out the square root of 16 or figure out what number squared equals 16 and we know that to be 4. so amplitude is going to be divided by 4 and we get 0.3 so the most helpful thing that you can do to understand amplitude power and intensity relationship is to remember anything related to amplitude is amplitude squared power intensity are directly related to one another and know your squares so you can figure out what factors you will be dividing or multiplying by right so power and intensity are proportional to amplitude squared again we just need to calculate what the changes in amplitude square it and we know what the change will be in power and intensity opposite of that if we only have the change in power intensity we need to take the square root of that and that will be the amplitude factor power intensity are proportional to one another and increase decrease by the same factor i want to point out that at no point during this section have we talked about wavelength propagation speed frequency or period they are not related to those other four parameters so the bigness parameters hang out on their own no relation to the other four parameters and again just like the other math that i showed you this is probably way more math and you'll have to do as well but here's an example of a question that you might come across what if we ask you that the amplitude of a wave has increased from 4 megapascals to 8 megapascals what happened to the power well we can look at the numbers we have 4 to 8 which is a doubling or increasing by a factor of 2. and because amplitude increased by a factor of 2 and we know that power is proportional to amplitude squared then power should be increasing by a factor of 4 2 squared but we don't have 4 as an answer this is where knowing some different ways of saying different numbers is helpful so it doubled at half it quadrupled or it quartered in this case it quadrupled is correct because it increased four times so again go ahead and pause the video and get ready to do your workbook practice moment on the practice you'll see a chart in which i have given you original values for amplitude power and intensity and you'll use the chart to fill in the blanks for the new values and here are the answers so you were filling in the values in the new values column the numbers that are bolded were given to you so in our first set we see that amplitude increased from three to nine so increase by a factor of three which means that we need to multiply intensity and power by factors of nine the second set shows us that 3.6 reduced to 0.9 and because amplitude decreased by a factor of 4 both intensity and power will decrease by a factor of 16. so we need to take the original values and divide them by 16. the third set shows us that power increased from 3 milliwatts to 75 milliwatts that is increasing by a factor of 25. well intensity and power are proportional to one another so intensity also increases by a factor of 25 so we multiply 1 by 25 now the trickier side of that is to figure out what happened to amplitude 5 times 5 is 25 or 5 squared so knowing that we know then that amplitude would increase by a factor of 5 to mean that power and intensity increase by a factor of 25 so we multiply 5 times 2 and get 10 megapascals now the last set shows us that intensity decreased from 180 down to 5. so 180 down to five is a decrease in a factor of 36 so because intensity decreased by a factor of 36 power should also decrease by a factor of 36 so we divide 540 by 36 to get 15 milliwatts and again to figure out what has to happen to amplitude we have to find the number that equals 36 when squared and 6 times 6 is 36 so amplitude decreases by a factor of 6 so 12 divided by 6 gives us 2. and you guys we did it we finished up our seven parameters of sound just to recap very quickly we have amplitude power and intensity all determined by the machine controlled by the sonographer but attenuate in the body and they're all directly related to one another remember amplitude squared in relationship to the other two period and frequency come next they are also specially related to each other as reciprocals they're only controlled by the machine and cannot be adjusted wavelength is up next remember that it is dependent on the machine and the medium it cannot be adjusted and is directly related to speed but inversely related to frequency and lastly we have propagation speed which is only dependent on the medium it also cannot be adjusted it has in average in soft tissue at 1540 meters per second and it is directly related to stiffness but inversely related to density be sure to work through the activities in your workbook and go through your nerd check to evaluate your knowledge of the seven sound parameters