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\bullet Ultrasound in medicine. A 2.00 $\mathrm{MHz}$ sound wave travelsthrough a pregnant woman's abdomen and is reflected from the fetal heart wall of her unborn baby. The heart wall is moving toward the sound receiver as the heart beats. The reflectedsound is then mixed with the transmitted sound, and 85 beatsper second are detected. The speed of sound in body tissue is1500 $\mathrm{m} / \mathrm{s} .$ Calculate the speed of sound in body tissue isinstant this measurement is made.

3.19 $\mathrm{cm} / \mathrm{s}$

Physics 101 Mechanics

Chapter 12

Mechanical Waves and Sound

Periodic Motion

Mechanical Waves

Sound and Hearing

Simon Fraser University

Hope College

University of Sheffield

University of Winnipeg

Lectures

08:15

In physics, sound is a vib…

04:49

In physics, a traveling wa…

07:46

Ultrasound in Medicine. $\…

0:00

A 2.00-MHz sound wave trav…

03:14

The Doppler effect using u…

03:30

A source of ultrasound emi…

02:08

Ultrasound is used in medi…

02:38

08:28

A $\textbf{Doppler flow me…

01:48

Ultrasound Imaging. Sound …

Doppler ultrasound is used…

07:38

(III) The Doppler effect u…

01:23

Ultrasound with a frequenc…

02:10

$\bullet$$\bullet$ Heart s…

00:22

Sound waves with frequenci…

07:23

Obstetricians use ultrasou…

03:40

Physicians use high-freque…

08:21

An ultrasound unit sends a…

05:05

01:15

Sound having frequencies a…

06:32

Expectant parents are thri…

09:52

A diagnostic ultrasound ec…

So here we have the Doppler effect. And here the Doppler effect is causing the frequency of the listener sub to to be greater than the frequency of the source of one. We know that the frequency of else of one Elsa to rather minus the frequency of us someone equals 85 hertz. And then we can say that the frequency of the source of one equals two megahertz and this legal to 0.0 times 10 to the sixth, it hurts. So at this point, we can say that the first scenario, rather we want to find the speed, the velocity of the wall. So we're first going to say that the heart wall receives the sound So we can say that visa our equals negative velocity of the wall so we can set the frequency of the listener equals thieve a las ity plus the velocity listener to write about the velocity plus the velocity of the source times frequency, the source. We're going to relate to this situation. So the velocity of the listener said one equals the velocity took the velocity of sound through human tissue minus the velocity of the heart wall divided by the velocity of the sound through human tissue times the frequency of the source of one. Now this is going to be for Hartwall receives sound. Now it's going to new workbook and say that the heart wall makes the sound So we can say that the frequencies of two will be equal to the frequency of the listener. Someone ah, we can save the velocity of the source will be equal to positive b of the wall And you know that the velocity of the listener equals zero. So we consider the frequency of the listeners of two equals the velocity right about the velocity puts the velocity of the wall again. This is the velocity of sound through human tissue times the frequencies of two. We know that the frequencies of two equals if you can see else of one that we found here. So we're just simply going tio substitute And this will be velocity divided by the velocity plus the law times velocity minus philosophy of the world divided by the times the frequency of the source sub one And of course, the V's cancel out and we get the frequency of the listeners of two equals the the lost City minutes a velocity of the law divided by the velocity plus the velocity of the long again times the frequency of the source of one. So at this point, we can say that the frequency of the listener sub two minus the frequency of the source of one equals ah one minus the lost city must velocity of the wall divided by the velocity plus the velocity of long with the heart wall. And this will be frequencies of one. Now, um, we can say that Ah, frequency else to minus frequency. Source up one equals, um, two times the velocity of the heart wall divided by the velocity through human tissue plus the velocity of the law times the frequency sub one. And at this point, we can solve for the world. So the velocity of the law. So we know that the velocity of the wall is going to be equal to two times the frequency of the source of one minus the frequency of the listener sub one minus the frequency of the source of one. Ah, and then the velocity of sound through human tissue times the frequency of the listeners too, minus the frequency of the A source. Someone we know that the frequency of the source of one is much, much greater than the frequency of the listener Sub two minus the frequency of the source of one. So we can actually eliminate that sort of that entire now that we can eliminate that entire term. And so the new equation the velocity of the war will now be equal to frequency l sub to most recon cs of one and then times V and then divided by two times the frequency sub one. So essentially, this term is eliminated, and at this point, we can actually solve. So it'll be 85 hertz times 1,500 meters per second, divided by two times the ah, two megahertz. So two times 2.0 times 10 26 hertz. And we find that the velocity of the wall is going to be equal to 0.319 meters per second. So that be the velocity of the heart wall and our final answer that is the end of the solution. Thank you for watching

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