A man standing at a distance in front of a tall vertical cliff claps his hands and hears t… — JAMB UTME

A man standing at a distance in front of a tall vertical cliff claps his hands and hears the echo after $1.2\text{ s}$ . If the speed of sound in air is $340\text{ m/s}$ , what is the distance between the man and the cliff in meters?

Answer: 204 m

Answer

The distance between the man and the cliff is

204\text{ m}

An echo is formed when sound travels to an obstacle and reflects back. The time taken for the sound to travel to the cliff and back is

1.2\text{ s}

. The total distance covered by sound is

v \times t = 340\text{ m/s} \times 1.2\text{ s} = 408\text{ m}

. Since this distance covers two equal trips (to the cliff and back), the distance to the cliff is

408\text{ m} / 2 = 204\text{ m}

Step-by-Step Solution

State the relationship between sound speed, total echo time, and distance.

Total distance traveled by the sound is twice the distance to the cliff:

2d = v \times t

An echo involves sound traveling from the source to the reflecting barrier and back.

Substitute the given values into the equation.

2d = 340\text{ m/s} \times 1.2\text{ s} = 408\text{ m}

To find the total distance traversed by the sound wave.

Solve for the distance

d

d = \frac{408\text{ m}}{2} = 204\text{ m}

The one-way distance to the cliff is half of the total distance traveled by the echo.

Key Concept

Calculation of echo distance using

d = \frac{v t}{2}

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