Final answer:
The depth of the ocean is calculated by dividing the time for the sound to return by 2 to get the one-way travel time, and then multiplying by the speed of sound in water (1450 m/s). For a return time of 2.5 seconds, the depth would be 1812.5 meters.
Step-by-step explanation:
To determine the depth of the ocean at a particular point using sonar, a ship sends a signal to the bottom of the ocean which reflects back to the ship. The time taken for the sound wave to return is recorded. Since the speed of sound in sea water is known to be 1450 m/s, calculating the depth can be done using the formula Depth = Speed of Sound × (Time/2).
In the example provided, the signal took 2.5 seconds to return. To find the depth:
- First, divide the time by 2, which is 2.5 seconds / 2, to get the time taken for the sound to travel to the seabed. This value is 1.25 seconds.
- Then, multiply the time it takes for the sound to travel to the seabed (1.25 seconds) by the speed of sound in sea water (1450 m/s) to get the depth.
- The resulting calculation would be 1.25 seconds × 1450 m/s = 1812.5 meters.
The depth of the ocean at that point is therefore 1812.5 meters.