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The time delay between transmission and the arrival of the reflected wave of a signal using ultrasound traveling through a piece of fat tissue was 0.13 ms. At what depth did this reflection occur?
Question by OpenStax is licensed under CC BY 4.0.
Final Answer

$9.4 \textrm{ cm}$

Note: In the video, the speed of ultrasound in fat is mistakenly given as 1540 m/s, whereas it should be 1450 m/s. The final answer of 10 cm is incorrect. The correct final answer is 9.4 cm. This video has been queue for a re-take, and also the closed captions need redoing. The calculator screenshot has been corrected.

Solution Video

OpenStax College Physics Solution, Chapter 17, Problem 75 (Problems & Exercises) (1:10)

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Calculator Screenshots

OpenStax College Physics, Chapter 17, Problem 75 (PE) calculator screenshot 1
Video Transcript

This is College Physics Answers with Shaun Dychko. An ultrasound wave is going to reflect off of some other type of tissue here that's probably an interface between two different media here. And so, it's causing a reflection. And then the reflection is detected here. And so, this sound has to travel through the tissue twice. And so, it covers the tissue thickness twice. So this total distance that it covers is two times <i>D</i>, and it does so on a certain time. And this total distance over time is the speed of the ultrasound. Now, we're given what the speed of the sound is, and we know the time as well, and so we'll solve this for <i>D</i>. We'll multiply both sides by <i>T</i> over two, and we end up with this line here. Switching the sides around as well, so we have <i>D</i> over <i>V</i> <i>T</i> over two. So, the speed of sound in tissue is 1540 meters per second multiplied by 0.13 times ten to the minus three seconds, that's 0.13 milliseconds, written in seconds, and divided by two. And this is 0.1 meters, which is 10 centimeters. So, the tissue is 10 centimeters thick.


Submitted by Oli on Thu, 07/02/2020 - 06:58

I think fat is 1450, not 1540...

Submitted by ghanastudy on Thu, 07/02/2020 - 08:57

Yes, fast is 1450

Submitted by ShaunDychko on Thu, 07/02/2020 - 10:47

Hello Oli and ghanastudy,
Thank you both for noticing this! I have made a note below the final answer, and updated it to 9.4 cm, and updated the calculator screenshot. I've flagged the video for a re-take and I notice also that the closed captions need redoing.
Thanks again, and best wishes with your studies,