A hiker shouts toward a vertical cliff and the echo is heard 4 s later. If the speed of the sound in air is 343 m/s, what is the distance between the hiker and the cliff?

Steps to Solve

1. Calculate the total distance traveled by the sound The sound travels from the hiker to the cliff and back, so we can use the formula $ distance = speed \times time $ to find the total distance the sound traveled. Given: Speed of sound, $v = 343 , \text{m/s}$ Total time for the echo to return, $t = 4 , \text{s}$

Using the formula: $ d = v \times t $ $ d = 343 , \text{m/s} \times 4 , \text{s} $ $ d = 1372 , \text{m} $

2. Calculate the distance between the hiker and the cliff Since the sound travels to the cliff and back, the distance calculated in step 1 is twice the distance between the hiker and the cliff. To find the distance between the hiker and the cliff, we divide the total distance by 2. $ \text{Distance to cliff} = \frac{\text{Total distance}}{2} $ $ \text{Distance to cliff} = \frac{1372 , \text{m}}{2} $ $ \text{Distance to cliff} = 686 , \text{m} $