A person standing at a stationary position between two tall parallel vertical walls fires … — JAMB UTME

A person standing at a stationary position between two tall parallel vertical walls fires a starter pistol. The person hears the first echo reflected from the nearer wall after $1.2\text{ s}$ and the second echo from the farther wall after $1.8\text{ s}$ . Given that the speed of sound in air is $340\text{ m/s}$ , what is the total distance between the two walls in meters?

Cevap: 510 m

Cevap

The total distance between the two walls is

510\text{ m}

Because sound travels to each wall and reflects back to the observer, the distance to each wall is given by

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

. The distance to the nearer wall is

d_1 = \frac{340 \times 1.2}{2} = 204\text{ m}

, and the distance to the farther wall is

d_2 = \frac{340 \times 1.8}{2} = 306\text{ m}

. Since the observer is between the two walls, the total separation between the walls is

204\text{ m} + 306\text{ m} = 510\text{ m}

Adım Adım Çözüm

Calculate the distance from the observer to the nearer wall.

d_1 = 204\text{ m}

The sound travels to the nearer wall and back in

1.2\text{ s}

, covering twice the distance to that wall.

Calculate the distance from the observer to the farther wall.

d_2 = 306\text{ m}

The sound travels to the farther wall and back in

1.8\text{ s}

, covering twice the distance to that wall.

Add the two individual distances to find the total distance between the walls.

D = d_1 + d_2 = 510\text{ m}

The observer is positioned between the two walls, so the separation distance is the sum of both distances.

Anahtar Kavram

Echo and Speed of Sound Propagation between Parallel Boundaries

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