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

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