Transcription
Hello and welcome back. In the previous talk, we looked at what exactly sound is. We compared sound to electromagnetic radiation, and then we looked at some parameters of sound: the wavelength, the frequency, and the speed of sound.
Now, in this talk, we're going to look at wavelength and frequency in a little bit more depth and discuss a parameter known as the period. Then, we're going to spend the most of this talk looking at the speed of sound. And I've said before that the speed of sound is independent of frequency; it's determined by the material through which the sound is traveling. So, we're going to look at what properties of that material determine the speed of the sound.
Now, we've seen this diagram before: our sound wave going from left to right, this longitudinal wave, the units in this wave moving in the same direction as the energy transfer, and we've got regions of compression and rarefaction with local pressure changes that can be plotted on a sine wave here. Now, this sine wave, if we were to take successive peaks in this wave, the distance between that is known as the wavelength. The wavelength is measured in units of distances, an actual distance. We then discussed frequency, which is the number of cycles of a wave that pass a particular point in a given period of time, and we measure frequency in Hertz. We then looked at the speed of sound, which determines the distance traveled over a period of time by this sound wave.
Now, what is known as period is represented by the letter T here, this capital T. Now, period is inversely related to frequency. If we take one and divide it by the frequency in Hertz, we will get our period. Now, what exactly is period calculating? Period is the amount of time for one cycle of a wave to pass a particular point. It's measured in units of time. How long does one full cycle of the wave take to pass a particular point? And that's known as the period.
Now, these parameters are going to become critically important later on when we're talking about attenuation, when we're talking about how echoes are produced within the body, and how we go about creating our ultrasound image.
Now, when we looked at speed, we said that it's a function of frequency and wavelength. Now, unlike electromagnetic radiation, the speed changes depending on the medium through which that sound wave is traveling. What doesn't change is the frequency of that sound. If we were to set the ultrasound probe to a set frequency, no matter what material that wave is going through, the frequency will remain the same. The wavelength links our frequency and our speed. Frequency and speed are completely independent of one another. Speed is determined by the material; frequency is determined by us; wavelength is the glue that puts it together to ensure that this formula happens.
Now, you'll see in ultrasound, there are a lot of formulas that we are going to come across, and if you don't have this contextual understanding, you might be tempted to change this frequency when the wavelength changes. A common question in exams is, if the wavelength of a sound wave was to change, what would happen to the frequency? And it's tempting to say that as wavelength increases, frequency decreases. That's not the case. Frequency remains the same. The speed of sound will change.
So, I've mentioned that the speed of sound is dependent on the material through which it's traveling. Now, that goes without saying, there must be properties of that material that determine how quickly the sound wave travels through that material. And there are two major properties that we look at when calculating the speed of sound. The first is known as the elastic property of the material: how readily do the units in that material return to their resting place from where the energy is transferred to that unit? How quickly does it come back? How stiff is that tissue? The stiffer the tissue, the more readily that unit will come back to where it rested. How resistant is it to compression? The more a material is able to be compressed, the less stiff that material is.
Now, the stiffer a material is, the faster sound will travel through that material. The second property is known as the inertial property of that material. Now, inertia describes the amount of force that is required to move those units within the tissue. Now, the inertia is represented by the density of the tissue. The more dense tissue, the more tightly packed the units within that medium are, the more force or the more inertia that tissue has to propagate that energy through a tissue.
Now, this is where people often get confused. We often think that the denser a tissue, the faster sound will travel. We've always heard that sound travels quicker in water than it does in air, and we perhaps have thought that's because of the density of water. It's actually because of the elastic properties of those mediums. Water is less compressible; water is stiffer than air. The increase in density will actually lead to a slower speed of sound. If you were to take two materials that have the same elastic property, say dry air and humid air, the density of humid air is more than that of dry air. Now, sound will actually travel quicker in the dry air, the less dense material. This is really important to remember that the less dense air material is, the faster sound travels through that medium.
Now, the elastic property is what is known as the bulk modulus, and the inertial property as the density of the material. As I've said, the bulk modulus is the tissue stiffness, the resistance that tissue has to compression, how readily do the units come back to their resting place. The stiffer the tissue, the less compressible a tissue is, the higher the bulk modulus, the faster speed travels. The density is how tightly packed the particles are in that medium. The tighter they are packed in the medium, the slower sound will go through the tissue, the more inertia that tissue has.
Now, a lot of people find this confusing, and I find it really helpful to use the analogy of a running man. We've seen that the speed of sound is a function of the frequency of that sound and the wavelength of the sound. Now, if you take a runner who is running at a set cadence, their cadence doesn't change. They are the ultrasound machine making a set frequency. The number of steps that they take per minute remains the same, no matter what happens. They will be running at a set speed, and that speed is determined by the ground that they are running on and the air that they are running through.
Now, I like to think of bulk modulus as the ground that this runner is running on. The harder the ground, the stiffer or less compressible the ground is, the faster the runner will be running. If that runner is running at a set frequency and they're running on hard ground, their stride length will be longer; their wavelength will be longer; the distance that they take with each step will be longer. Now, if that hard ground was to abruptly end and it became sand, which is more compressible, less stiff, and the runner was running at the same rate, they would start to run slower on the sand, despite their frequency being the same. That sand is more compressible; it's less stiff; their bulk modulus of the sand has decreased. Now, their stride length has gotten shorter. The frequency is the same, but the wavelength, the stride length, has gotten shorter, and their speed has decreased.
Now, when we think of density, think of the air that the runner is running through. The thinner the air, the faster the runner will run. The lower the density of that air, the faster the runner will run. If that air was to be replaced with syrup, a much thicker, more dense material, the runner would run much more slowly, if their frequency, their steps per minute, was the same. The wavelength, or their stride length, would decrease drastically. So, as density increases, as the air gets thicker and thicker, the speed of that runner gets slower. The same happens in sound: as density of a tissue increases, the speed of sound decreases depending on that density.
Now, if we were to represent this in a graph, we can see that we've got various materials that we will find in clinical imaging, and we see that the speed of sound changes depending on those materials. Now, these materials, you might be confused and say, "But these materials are getting more and more dense. Why is the sound not getting less and less?" We said that as density increases, our speed decreases, and that's because the bulk modulus, in proportion to the density, increases at a much higher rate. It's important to know that bulk modulus and density are actually independent factors of one another. It just so happens that tissues that are more dense generally have a higher bulk modulus; they're stiffer tissues, more resistant to compression. So, remember this: it's the bulk modulus that accounts for this increase in speed. If the bulk modulus of all these tissues was exactly the same and only the density changed, the speed would actually decrease as we head down our table.
Now, when we are discussing ultrasound in this module, we are going to be building on this diagram here, so I want to introduce this diagram to you. When we take ultrasound images, we send a pulse of ultrasound into the tissue and then wait for that ultrasound to bounce off tissues. We're going to discuss exactly how that happens and why that happens in future talks. This is the period here of waiting; we are listening for those echoes to return back. We will then send another pulse of ultrasound and listen for that to come back. These type of waves create images. If we ever want to create an image, we both need to transmit ultrasound and then listen for that ultrasound to come back.
Now, there are various parameters that we are going to build on to this image here, and I want to include the parameters that we've discussed so far. Everything above this here is a time parameter, and everything below this line here is measured in distance. It's a distance parameter. And you'll see as we add more and more parameters, it becomes useful to separate them into time and distance. Anything on the plane of this line is a combination of both time and distance. So, we've discussed wavelength, the distance of one cycle in the wave. We've discussed frequency, the number of wavelengths that pass a particular point in a given period of time. We've discussed period, the time taken for one cycle to a particular point. And we've discussed speed, meters per second, distance per time, the distance traveled over a period of time.
Now, in our next talk, we are going to discuss sound intensity. We're going to look at the amplitude of the wave and how that affects the intensity of the wave, the amount of power that we emit into a tissue in a given area of tissue. So, I'll see you all in that talk. Goodbye, everybody.