To calculate the speed of the sound wave in the ocean, we can use the formula for speed:

$\text{Speed} = \frac{\text{Distance}}{\text{Time}}$

However, we need to account for the fact that the time given is for the round-trip travel of the sound wave. This means the sound wave travels from the submarine to the ocean floor and back. Therefore, the total distance traveled by the sound wave is twice the depth of the ocean, and the time represents the round-trip time.

Step 1: Determine the total distance traveled

The depth of the ocean floor is 324 meters. The total distance traveled by the sound wave (down and up) is:

$\text{Total distance} = 2 \times 324 \, \text{meters} = 648 \, \text{meters}$

Step 2: Use the time to calculate speed

The time for the round-trip is 0.425 seconds, so we now calculate the speed:

$\text{Speed} = \frac{\text{Total distance}}{\text{Time}} = \frac{648 \, \text{meters}}{0.425 \, \text{seconds}} \approx 1520 \, \text{m/s}$

Final Answer:

The speed of the sound wave in the ocean water is approximately 1520 meters per second.

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Would you like to go into more details about the calculation, or is there anything else you want to ask? Here are a few related questions you might find interesting:

1. How does the temperature of ocean water affect the speed of sound?
2. What happens to the speed of sound in a medium when its density changes?
3. How do sonar systems measure distances based on reflected waves?
4. What other factors could influence the speed of sound in water besides temperature and density?
5. How would you calculate the speed of sound in air using similar principles?

Tip: When calculating speed using round-trip time, always remember that the time given is the total for both the outward and return journeys!