Are concerned with determining the thickness d of a layer of soil that lies on top of

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Are concerned with determining the thickness d of a layer of soil that lies on top of a rock formation. Geologists send two sound pulses from point A to point D separated by a distance s. The first pulse travels directly from A to D along the surface of the earth. The second pulse travels down to the rock formation, then along its surface, and then back up to D (path ABCD), as in Figure 41. The pulse travels with velocity v1 in the soil and vin the rock.

A B S Soil Rock FIGURE 41 C D 0 d

In this exercise, assume that v2/v≥ √1 + 4(d/s)2.
(a) Show that inequality (1) holds if sin θ = v1/v2.
(b) Show that the minimal time for the second pulse is

2d t2 = VI -(1-k) /2+ S V2

where k = v1/v2.

(c) Conclude that t2 t 2d(1-k)/2 S - + k.

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Related Book For  answer-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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