An echo sounder on a fishing boat emits an acoustic pulse vertically downward toward the s… — JAMB UTME

An echo sounder on a fishing boat emits an acoustic pulse vertically downward toward the seabed and detects the reflected signal $0.80\text{ s}$ later. If the speed of sound in seawater is $1450\text{ m/s}$ , what is the depth of the sea in meters at this location?

Answer: 580 m

Answer

The depth of the sea is

580\text{ m}

An echo signal travels to the reflecting surface and back, covering twice the depth (

2d = v \times t

). Substituting

v = 1450\text{ m/s}

and

t = 0.80\text{ s}

gives

2d = 1160\text{ m}

, so the seabed depth

d = 580\text{ m}

Step-by-Step Solution

Identify the given physical quantities

Total travel time

t = 0.80\text{ s}

and speed of sound

v = 1450\text{ m/s}

An echo involves sound traveling to the seabed and back, so the recorded time represents a two-way journey.

Set up the distance equation for an echo

Total distance traveled by the sound pulse is

2d = v \times t

Sound travels to the sea floor and reflects back to the ship, covering a total distance equal to twice the depth.

Calculate the depth

d

d = \frac{1450 \times 0.80}{2} = 580\text{ m}

Dividing the total round-trip distance by 2 yields the one-way depth.

Key Concept

Calculation of distance using sound echoes in a medium

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