OpenStax College Physics, Chapter 17, Problem 75 (Problems & Exercises)

This is College Physics Answers with Shaun Dychko. Ultrasound is being transmitted through a layer of fat and then it reflects off of this interface between media— there must be some other type of tissue down here— it reflects off that and then goes back to the beginning where there's also a detector so this wand that the technician puts on the tissue has both a transmitter of ultrasound and a microphone to detect the return signal. So it has to travel through this fat layer twice so we will say that the fat layer has a thickness—we will call it d— and so the total distance that's being traveled is 2 times d because once down and then again back up and I have drawn it on an angle here so that just to make it clear that the signal goes down on the one hand and then back up and this path length is greater than d... this is, you know, the hypotenuse of this triangle here but we will just ignore that... imagine that it's going straight down and then straight back up... I did it at an angle just for illustration purposes. So the sound has to go 2 times the thickness of the fat and then that's divided by time gives us this speed. Now we know the speed because we can look that up in table [17.5]— the speed of ultrasound in fat tissue is 1450 meters per second. So we can rearrange this to solve for d, which is the thickness of the fat, which is what we want to know so we multiply both sides by t over 2 and then switch the sides around and we are left with d equals vt over 2. So that's 1450 meters per second— speed of ultrasound in fat— times the time of 0.13 milliseconds, which is times 10 to the minus 3 seconds, divided by 2 and that's 0.09425 meters, which we convert into centimeters by multiplying by 100 centimeters for every meter and after rounding, we get 9.4 centimeters.