Sound travels much farther in water than light, and thus, is used for various underwater applications. A sonar signal sent to find the depth of ocean takes 4 s to return. What is the depth of the ocean at that location if the speed of sound in seawater is 1500 m s⁻¹?
3000 m
Explanation
This numerical follows the same logic as Example 10.6 in the textbook. The sonar signal travels from the source to the ocean floor and reflects back, so the total time of 4 s is for the round trip. The time to reach the ocean floor is half of the total time. Using the formula distance = speed × time, we calculate the depth.
Solution Steps
Given: Total time for the sonar signal to return = 4 s; Speed of sound in seawater = 1500 m s⁻¹
Time taken to reach the ocean floor = Total time / 2 = 4 s / 2 = 2 s
Depth of the ocean = Speed × Time = 1500 m s⁻¹ × 2 s = 3000 m