When needed, use 340 m/s for the speed of sound and 3.00 x 108 m/s for the speed of light.
A hiker determines the length of a lake by listening for the echo of her shout reflected by a cliff at the far end of the lake. She hears the echo 2.20 s after shouting. How long is the lake?
her shot travels down the lake, and the echo travels back
... total distance (and time) is two lake lengths
length = (2.20 s * 340 m/s) / 2
To determine the length of the lake, we need to find the time it takes for the sound to travel to the cliff and back. We know the speed of sound is 340 m/s, so we can use the formula: distance = speed × time.
Let's break down the problem:
1. The hiker shouts, and the sound travels to the cliff.
2. The sound then reflects off the cliff and travels back to the hiker.
3. The hiker hears the echo 2.20 s after shouting.
Since the sound travels to the cliff and back, we need to divide the total time by 2 to find the time it takes for each leg of the journey.
Time for one leg of the journey = 2.20 s ÷ 2 = 1.10 s.
Now we can use the formula to find the distance:
Distance = speed × time = 340 m/s × 1.10 s.
Calculating this: Distance = 374 m.
Therefore, the length of the lake is 374 meters.