A hiker standing at a distance from a tall vertical cliff shouts and hears an echo 0.60\te… — JAMB UTME

A hiker standing at a distance from a tall vertical cliff shouts and hears an echo $0.60\text{ s}$ later. If the speed of sound in air is $330\text{ m/s}$ , what is the distance between the hiker and the cliff?

A
$198\text{ m}$
$99\text{ m}$ Answer
C
$550\text{ m}$
D
$49.5\text{ m}$

Answer

The distance between the hiker and the cliff is

99\text{ m}

An echo is a reflected sound wave. The sound travels from the hiker to the cliff and back, covering a total distance of

2d

in time

t

. Therefore,

2d = v \times t

, which gives

d = \frac{330\text{ m/s} \times 0.60\text{ s}}{2} = 99\text{ m}

Step-by-Step Solution

Identify given parameters and echo relation

Speed of sound

v = 330\text{ m/s}

, time elapsed

t = 0.60\text{ s}

. An echo involves sound traveling to the wall and back (

2d

The total distance traveled by the sound wave during time

t

is twice the distance to the reflecting surface.

Calculate the one-way distance

d = \frac{v \times t}{2} = \frac{330 \times 0.60}{2} = 99\text{ m}

Dividing the total distance by 2 yields the actual distance from the hiker to the cliff.

Key Concept

Echo distance calculation

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic