Physics

Problem

The upper

300\,\text{m}

of ocean water near a ship has a temperature at which sound travels at

1520\,\text{m/s}

. Below this layer, colder water makes the speed of sound

1480\,\text{m/s}

. A sound pulse sent vertically downward is received back after a total time of

1.20\,\text{s}

. Assuming the pulse travels straight down, reflects once from the sea floor, and returns along the same path, calculate the depth of the sea floor.

Intuitive explanation

This is a layered-medium travel-time problem where sound moves at different speeds through two distinct regions. The key insight is to split the journey into segments: the pulse travels down through the warm layer at one speed, then through the cold layer at a slower speed, bounces off the bottom, and retraces its path back up. Since you know the total round-trip time and the speed in each layer, you can set up equations for the distance traveled in each region—the warm layer's distance is fixed at 300 m, but the cold layer's depth is unknown and determines the total sea floor depth.

Intuitive explanation

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