Geologists use explosives to map the subterranean. The times for the reflected waves to arrive at a monitoring station can tell a great deal about the composition of the rock structures. Suppose the time it takes for a wave that is reflected from the interface of (1) and (2) is 2 s, and the time for another wave that is reflected between (2) and (3) is 2.5 s and the speed of the wave in layer (1) is 6 km/s and in layer (2) is 4 km/s, how thick is layer (2)?
A) 2 km
B) 1 km
C) 3 km
D) 6 km
E) 8 km

Question

Geologists use explosives to map the subterranean. The times for the reflected waves to arrive at a monitoring station can tell a great deal about the composition of the rock structures. Suppose the time it takes for a wave that is reflected from the interface of (1) and (2) is 2 s, and the time for another wave that is reflected between (2) and (3) is 2.5 s and the speed of the wave in layer (1) is 6 km/s and in layer (2) is 4 km/s, how thick is layer (2)? 
A) 2 km 
B) 1 km 
C) 3 km 
D) 6 km 
E) 8 km

Quizplus · Accepted Answer

We can use the formula:

time = distance / speed

to determine the thickness of layer (2). Let's assume the thickness of layer (1) is x.

For the wave reflected between (1) and (2):

2 = (x + d) / 4    (where d is the thickness of layer (2))

For the wave reflected between (2) and (3):

2.5 = (2d) / 6

Solving for d in the second equation, we get:

d = 7.5 km

Substituting d into the first equation and solving for x, we get:

x = 25 km

Therefore, the thickness of layer (2) is:

d = 2x - 50 = 1 km

So the answer is B) 1 km.

Geologists Use Explosives to Map the Subterranean