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Problem 22 Hard Difficulty

A narrow beam of ultrasonic waves reflects off the liver tumor in Figure P22.22. If the speed of the wave is 10.0% less in the liver than in the surrounding medium, determine the depth of the tumor.

Answer

$\text { The depth of the tumor is } 6.3 \mathrm{cm}$

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Top Physics 103 Educators
Andy C.

University of Michigan - Ann Arbor

Marshall S.

University of Washington

Aspen F.

University of Sheffield

Jared E.

University of Winnipeg

Video Transcript

So, given the information, our question wants us to determine the depth of the tumor. Okay, so to do that, we need to figure out the angle Fada to here in this image. So the speed, um, of the, uh, the index of refraction of the liver is the first thing we need to find. And we can do that using the fact that the speed in the medium of air uh V a divided by the speed of the medium in the liver who call that V l is equal to the index of refraction in the liver. We'll call that insa bell defined by the index of refraction of air. And we were told that the so this is equal to V A. And we were told that the speed of the light in the liver is 90% of that in air. So this is 0.9 the A. So the d A. Is cancel. We find that in L in Seville is equal to one divided by 0.9, which is 1.11 So now we know the index of refraction of the liver. Since we know that we can go ahead and ah, find the angle of refraction here. So signed data too. Well, the ratio of science data one divided by science. A tatoo is equal to into over in one. Okay, well, here too is liver, and one is air. So I think the angle on the liver is equal to the inverse side of sign. Well, uh, and some a times sign of the incident angle with recalled data one which we go back was equal to 50 degrees divided by in Seville, which we found to be 1.11 So we find this angle equals 43 0.6 degrees. Now that we know that we can use our triggered a metric identity which says that the tangent of that angle, which we call status of l, is equal to the distance a b which we know was six centimeters divided by the distance. Oh, a which we want to find therefore, the distance Oh, a is equal to a be divided by the tangent of fate. A two but just 6.31 centimeters. If we can go ahead and box in is the solution to our question. Go

University of Kansas
Top Physics 103 Educators
Andy C.

University of Michigan - Ann Arbor

Marshall S.

University of Washington

Aspen F.

University of Sheffield

Jared E.

University of Winnipeg