How to Calculate the Distance of an Exploding Ship Underwater
What is the scenario presented in the data?
A navy diver hears the underwater sound wave from an exploding ship across the harbor. How far away is the ship?
Answer
The distance between the navy diver and the ship is 1.8 km.
When a navy diver hears the underwater sound wave from an exploding ship, it is essential to calculate the distance between the diver and the ship. In this scenario, the speed of sound in water is 1440 m/s, and the time taken for the sound wave to reach the diver through the air is 4.00 s.
To calculate the distance, we can use the formula:
s = vtWhere: s = distance, v = speed, t = time
For water, the formula becomes:
s = v_wt (eq 1)Where: v_w = speed of sound in water
For air, the formula is:
s = v_a(t + 4s) (eq 2)Where: v_a = speed of sound in air
By comparing equation 1 and equation 2, we can solve for the time taken by the sound wave, which is 1.25 s. Plugging this value back into equation 1, we find that the distance between the ship and the navy diver is 1.8 km.