(II) A sailor strikes the side of his ship just below the...

(II) A sailor strikes the side of his ship just below the
surface of the sea. He hears the echo of the wave reflected
from the ocean floor directly below 2.8 s later. How deep is the
ocean at this point?

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Key Concepts

Round-Trip Travel Time

In echo-based measurements, the total time recorded is for the sound wave's journey to the reflecting surface and its return to the source. This round-trip time must be divided by two to accurately compute the one-way distance to the reflecting surface.

Distance Calculation Using Time and Speed

This principle employs the basic relationship where distance equals speed multiplied by time. In echo problems, since the signal covers the distance twice, it is essential to adjust the calculation accordingly, highlighting the importance of correctly interpreting the measured travel time.

Reflection of Sound Waves

This concept explains how sound waves, when encountering a boundary like the ocean floor, bounce back towards their source. Understanding reflection is key to interpreting echoes, which are used to determine distances in environments where direct measurement is not feasible.

Speed of Sound in Water

Sound travels at a specific, typically higher, speed in water compared to air—around 1500 m/s. This known value is crucial in calculations requiring the relationship between travel time and distance, as the speed directly influences the measurement accuracy.

Transcript

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