Final answer:
To calculate the ocean's depth using sonar, halve the total signal return time and multiply by the speed of sound. The ocean's depth beneath the ship is 1,338.75 meters.
Step-by-step explanation:
To determine the depth of the ocean using sonar, you need to consider the time it takes for a sonar signal to travel to the ocean floor and back. Since the speed of sound in seawater is given as 1,530 m/s, we can calculate the distance the sound wave traveled and then half it to find the depth.
The formula to find the distance is Distance = Speed × Time. Since the signal has to travel to the bottom and back, the time we use in the calculation is half of the total time it takes for the signal to return.
In this case, the total time is 1.75 seconds, so the time one way is 1.75 s / 2 = 0.875 s. Now, using the formula:
Distance one way = Speed × Time
Distance one way = 1,530 m/s × 0.875 s
Distance one way = 1,338.75 m
Therefore, the depth of the ocean at that point is 1,338.75 meters.