Question

A group of hikers hears an echo 2.10 s after shouting. How far away is the mountain that reflected the sound wave? (Assume the speed of sound is 348 m/s.)

________m

Answer 1

Approximately
`365\; {\rm m}`.

Step-by-step explanation:

Let
`d` denote the distance between the hikers and the mountain.

The sound wave from the hikers need to travel a distance of
`d` to reach the mountain. The echo comes back at the hikers almost immediately after that and would need to travel the same distance,
`d\!`, to reach the hikers.

Hence, the
`t = 2.10\; {\rm s}` between the shout and the echo is the time it takes for sound to travel a distance of
`2\, d`- twice the distance between the hikers and the mountain.

Distance that sound travels in
`t = 2.10\; {\rm s}`:

`\begin{aligned} s &= v\, t \\ &= 348\; {\rm m\cdot s^(-1)} * 2.10\; {\rm s} \\ &= 730.8\; {\rm m} \end{aligned}`.

The distance
`d` between the hikers and the mountains would be:

`\begin{aligned} d &= (s)/(2) \\ &= \frac{730.8\; {\rm m}}{2} \\ &\approx 365\; {\rm m}\end{aligned}`.