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assuming the speed of sound in the ocean is 1.5 km/s, and standing on a ship you measure a two-way travel time of 10 seconds, what is the depth of the ocean below you?

User Ingemar
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Final answer:

To determine the depth of the ocean below a ship using the time for a sound signal to return and the speed of sound, multiply the sound speed by half the total travel time. Given a speed of 1.5 km/s and a two-way travel time of 10 seconds, the calculation shows the ocean's depth is 7500 meters.

Step-by-step explanation:

To calculate the depth of the ocean below the ship, we will use the two-way travel time of the sound and the known speed of sound in the ocean. Since the speed of sound in the ocean is given as 1.5 km/s, and the two-way travel time is 10 seconds, we can apply the formula: Depth = Speed × (Travel Time / 2). Calculations should be done in compatible units, so we use 1.5 km/s, which is equivalent to 1500 m/s.

First, we find the total distance traveled by the sound wave by multiplying the speed of sound by the travel time:

  1. Total distance = Speed of sound × Travel time
  2. Total distance = 1500 m/s × 10 s
  3. Total distance = 15000 meters

Since this distance is the total distance which includes the travel time to and from the ocean floor, we must divide it by 2 to find the one-way travel distance, which is the depth of the ocean:

  1. Depth of the ocean = Total distance / 2
  2. Depth of the ocean = 15000 m / 2
  3. Depth of the ocean = 7500 meters

Therefore, the depth of the ocean at that point is 7500 meters.

User Yusufk
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