A naval research vessel uses active sonar to determine the depth of the ocean floor. The s… — Armed Services Vocational Aptitude Battery (ASVAB)

A naval research vessel uses active sonar to determine the depth of the ocean floor. The ship's transducer transmits an acoustic pulse downward into seawater where sound travels at an average speed of $1{}500\text{ m/s}$ . If the reflected echo is recorded by the receiver exactly $4.0\text{ seconds}$ after transmission, what is the depth of the ocean floor?

A
$6{}000\text{ meters}$
B
$750\text{ meters}$
$3{}000\text{ meters}$ Answer
D
$375\text{ meters}$

Answer

3{}000\text{ meters}

Sonar relies on reflected sound waves (echoes). Because the sound pulse must travel down to the seafloor and then back up to the ship's receiver, the

4.0\text{ seconds}

represents two-way travel time. The one-way travel time is

2.0\text{ seconds}

. Multiplying the speed of sound in seawater (

1{}500\text{ m/s}

) by the one-way time (

2.0\text{ s}

) gives an ocean depth of

3{}000\text{ meters}

Step-by-Step Solution

Calculate the total distance traveled by the sound wave during the round trip

\text{Total distance} = \text{speed} \times \text{total time} = 1{}500\text{ m/s} \times 4.0\text{ s} = 6{}000\text{ meters}

The acoustic pulse travels from the ship down to the ocean floor and reflects back up to the surface.

Divide the total round-trip distance by two to obtain the one-way depth

\text{Depth} = \frac{6{}000\text{ m}}{2} = 3{}000\text{ meters}

Sonar distance measurement involves two equal legs of travel (downward and upward).

Key Concept

Calculation of distance using sound wave reflection and two-way travel time

Estimated Time:1m 0s

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