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 v₂ in the rock.

(a) Show that the time required for the first pulse to travel from A to D is t₁ = s/v₁.
(b) Show that the time required for the second pulse is

provided that

(c) Show that t₂ is minimized when sin θ = v_1/v₂.

Transcribed Image Text:

A B S Soil Rock FIGURE 41 C D 0 d