A girl stands at a specific distance from a flat vertical wall and claps her hands once. I… — JAMB UTME

A girl stands at a specific distance from a flat vertical wall and claps her hands once. If she hears the echo $0.4\text{ s}$ later, what is her distance from the wall in meters? (Take the speed of sound in air as $340\text{ m/s}$ )

Answer: 68 m

Answer

The distance of the girl from the wall is

68\text{ m}

An echo involves the sound traveling to the reflecting surface and returning to the source, covering a total distance of

2d

. Using

2d = v \times t

, we obtain

d = \frac{340 \times 0.4}{2} = 68\text{ m}

Step-by-Step Solution

Identify the given values from the problem statement.

Time for echo

t = 0.4\text{ s}

, speed of sound

v = 340\text{ m/s}

An echo is a reflected sound wave that travels to the wall and back, completing a round trip.

Apply the echo calculation formula.

d = \frac{v \times t}{2}

The total distance traveled by the sound is

2d

. Thus, the one-way distance

d

to the reflecting surface is half of the total distance.

Substitute the values and calculate the distance.

d = \frac{340 \times 0.4}{2} = 68\text{ m}

Multiplying the speed by half the elapsed time gives the distance to the wall.

Key Concept

Echo distance calculation

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