An oceanic depth-sounding vessel surveys the ocean bottom...

An oceanic depth-sounding vessel surveys the ocean bottom with ultrasonic waves that travel at $1530 \mathrm{~m} / \mathrm{s}$ in seawater. Show that when the time delay of an echo to the ocean floor below is $4 \mathrm{~s}$, the depth of the water is $3060 \mathrm{~m}$.

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Key Concepts

Echo Sounding Technique

Echo sounding is a measurement method that uses the reflection of sound waves to determine distances, especially in underwater applications. By sending a sound pulse and timing its return after reflecting off a surface, the distance to that surface can be accurately calculated using the speed of sound in the medium.

Round-Trip Travel Time

When using echo-based measurements, the time delay recorded is for the wave to travel to an object and back again. Recognizing that this time represents a round-trip journey is crucial, as the one-way distance (such as depth) must be determined by halving the total traveled distance.

Wave Propagation and Time-Distance Relationship

This concept involves understanding that distance can be calculated by multiplying the speed of a wave by the time it takes to travel that distance. In problems involving signal echoes, this relationship is used to compute the total distance traveled by the wave.

Speed of Sound in Fluids

This concept refers to the rate at which sound waves travel through a medium, such as seawater. The speed of sound depends on the properties of the medium, including its density and elasticity, and is fundamental to calculating distances based on the propagation of sound waves.

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