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(II) An airplane travels at Mach 2.0 where the sp…

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Problem 71 Hard Difficulty

(III) The Doppler effect using ultrasonic waves of frequency
$2.25 \times 10^{6} \mathrm{Hz}$ is used to monitor the heartbeat of a fetus. A
(maximum) beat frequency of 260 $\mathrm{Hz}$ is observed. Assuming
that the speed of sound in tissue is $1.54 \times 10^{3} \mathrm{m} / \mathrm{s},$ calculate
the maximum velocity of the surface of the beating heart.

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Physics 101 Mechanics

Physics for Scientists and Engineers with Modern Physics

Chapter 16

Sound

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Video Transcript

in this problem, we are asked to find calculate, Um, the heart, the hurt speed or the, um the maximum lost you off the surface off the hurt beaching we edge. We can find every Etch by using a Doppler formulas or Doppler shifts. Um, in this case, we have, ah, two Doppler ships. So one is for heart receiving the original signal so hard he's receiving a signal. Are receiving a signal receiving a signal. And in second case, um, detector is receiving the reflect reflected signal. So detector is receiving their reflected detector receiving a reflected signal. You have two cases we can write. Their frequency for the hurt is ah the original frequency if, lord, um into one minus, um, the lost t off the herd over the speed of the sound. Uh, then weaken right Also for the frequency off a detector, which is a dt d e t. That is equal to, um their frequency off the hurt. We just wrote it abo over, um, one plus of lost e off the hurt over the sound speed. So here f etch daesh street value off this year and the resultant if dish we get here is if Lord original frequency original into the speed of the sound minus the speed off the herd or the velocity off the hurt or, uh, speed off the sound. Plus, uh, lost off the hurt most of the herd, then the difference off frequencies here will be equal to. So the difference of frequencies will be equal to the F original. Do the frequency off the detector detector. Dee dee. Um, we will substitute this value here and subtract that from, if not, then our expression takes the form off. Takes the form. Uh, if Lord Times two, uh, we lost, you're hurt or ah, the speed of the sound. Plus, I lost you off the hurt from here. We will solve for the edge. Of course, that's what we need. Then the expression becomes, um, speed off a sound times the delta F change in frequency or, um, two times off. Original frequency minus changing frequency. Here, here we get the final expression. Now we will substitute the values s o. The values we have here is of course, the speed off the sound. Here we go already. The delta, if we have is a 2 60 hertz do 60 yards or, um, two times. Original frequency. Lord, no frequency we have Here is a dew 0.25 times 10 to the ball where six 10 to the power six hearts s 2.25 megahertz, actually minus the difference of frequency to 60. And, um, solving this expression, the final answer we get for the velocity off the hurt here is a 2.9 times 10 to the power minus two minus. To meet your per second or in centimeters, we can write 8.85 So this will be it born to page five centimeter per second. Centimeters per second. End off the problem. Thank you.

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Physics for Scientists and Engineers with Modern Physics

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Problem

(II) An airplane travels at Mach 2.0 where the sp…

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Related Courses

Physics for Scientists and Engineers with Modern Physics

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Discussion

Top Physics 101 Mechanics Educators

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Watch More Solved Questions in Chapter 16

Video Transcript

Douglas C. Giancoli

Physics for Scientists and Engineers with Modern Physics

Christina Krawiec

Marshall Styczinski

Zachary Mitchell

Meghan Miholics

This textbook answer is only visible when subscribed! Please subscribe to view the answer

Physics for Scientists and Engineers with Modern Physics

Christina Krawiec

Marshall Styczinski

Zachary Mitchell

Meghan Miholics

Douglas C. GiancoliPhysics for Scientists and Engineers with Modern Physics

Christina Krawiec

Marshall Styczinski

Zachary Mitchell

Meghan Miholics

Douglas C. Giancoli

Physics for Scientists and Engineers with Modern Physics