A hiker shouts toward a vertical cliff 633 m away. The echo is heard 4.0 s later. What is the speed of sound in air?

Question

Group of answer choices

271 m/s

361 m/s

190 m/s

317 m/s

Answer 1

To find the speed of sound in air, we can use the information given about the distance to the cliff and the time it takes for the echo to be heard.

1. The distance to the cliff is 633 meters.
2. The hiker shouts, and the sound travels to the cliff and back. Therefore, the total distance traveled by the sound is \(2 \times 633 , \text{m} = 1266 , \text{m}\).
3. The time taken for the echo to return is 4.0 seconds.

Now we can use the formula for speed, which is:

\[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} \]

Plugging in our values:

\[ \text{Speed} = \frac{1266 , \text{m}}{4.0 , \text{s}} = 316.5 , \text{m/s} \]

Rounding to the nearest whole number, the speed of sound in air is approximately 317 m/s.

Thus, the correct choice is:

317 m/s.