Question

Oil explorers set off explosives to make loud sounds, then listen for the echoes from underground oil deposits. Geologists suspect that there is oil under 500-m-deep Lake Physics. It's known that Lake Physics is carved out of a granite basin. Explorers detect a weak echo 0.99 s after exploding dynamite at the lake surface. The speed of sound

Answer 1

Answer:

dg= 942m

Explanation:

given the depth of the granite Us dg = 500m

time between the explosion t = 0.99s

the speed of sound in granite is Vg = 6000m/s

First of all calculate the time it takes the sound waves to travel down through the lake

Vw = dw/t1

t1 = dw/Vw

t1 = 500/1480

t1 = 0.338s.

Let dg be the depth of the granite basin, so the time it takes for the sound to travel down through the granite is t2 = dg/6000m/s......equation(1)

So the total time it takes to travel down to the oil surface will be

t1/2 = t1 + t2

t1/2=  0.338 + dg/6000.

since the reflection on the oil does not change the speed of sound, the sound will take travelling upto the surface the same time it takes to reach the oil

so; t = 2 t1/2

t1/2 = t/2 = 0.99s/2 = 0.495

Now insert into the values of t1/2 into the equation (1) and solve for dg;

we get 0.495 = 0.338 + dg/6000

dg = (0.495 - 0.338) x 6000

dg = 942m.

Answer 2

Answer:

d(g) = 642m

Explanation:

Given the following data

Depth of the granite d(g) = 500m, the time within the explosion (t) = 0.99secs.

From the fixed parameters, Speed of sound of granite = 1600m/s and speed of sound in water = 1480m/s.

Since it takes 0.99secs time of echo after exploding dynamite at the lake surface at 500m deep lake water, we have to calculate the time it takes for the sound wave to travel down the water

T(w) =  d(w)/V(w) = 500/1480

T(w) = 0.388secs

d(g) is the Depth of the granite and we calculate this as

T(2) = d(g)/6000

Therefore, the total time it takes for oil to flow down is given as

To = T(1)+T(2) = 0.388+d(g)/6000....1

Since the reflection of the oil doesn't change speed of the sound, we have that T = 2To

To = t/2 = 0.99/2

To = 0.495secs

Now, we plug in the values into equation 1

0.495 = 0.388+d(g)/6000

0.495-0.388 = d(g)/6000

0.107×6000 = d(g)

d(g) = 642m