Question

While hiking through a mountain, a climber lets out a scream. An echo (reflection of the scream off a nearby mountain) is heard $0.82s$ after the scream. The speed of the sound wave in air is $342m{s}^{-1}$ . Calculate the distance of the climber from the nearby mountain.

Answer 1

Step 1: Given data-

Time required for the echo to be heard $\left(t\right)=0.82s$

Speed of sound in air $\left(v\right)$ = $342m/s$

Let the distance of the climber from the mountain be $d$.

Step 2: Calculate the total distance traveled by sound:

We know that $speed=\frac{dis\tan ce}{time}$

Let $‘D’$ be the total distance travelled by sound

So, $D=v\times t$

On substituting given values:

$D=342\times 0.82=280.44m$

Step 3: Calculate the distance of the mountain from the climber:

The echo heard is a reflection of the scream $i.e.,$ sound travels to the mountain, gets reflected from it, and then travels back to the climber. So, the sound covers twice the distance to the mountain before the echo is heard.

$\therefore d=\frac{D}{2}$

Substituting the above-obtained values:

$d=\frac{280.44}{2}=140.22m$
Hence, the climber is $140.22m$ away from the nearby mountain.