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 1.7 s after shouting. Estimate the length of the lake.
To estimate the length of the lake, we need to consider the time it takes for the sound to travel from the hiker to the cliff and back as an echo.
The speed of sound in air is about 343 meters per second. Since the sound has to travel twice the distance from the hiker to the cliff, we can assume that the sound travels at a speed of 343 m/s * 2 = 686 m/s.
Given that the hiker hears the echo 1.7 seconds after shouting, we can use the equation: distance = speed * time.
The total distance traveled by the sound can be calculated as distance = 686 m/s * 1.7 s = 1166.2 meters.
Therefore, we estimate that the length of the lake is approximately 1166.2 meters.
To estimate the length of the lake, we can use the speed of sound and the time it takes for the echo to reach the hiker.
1. The speed of sound is approximately 343 meters per second (m/s) at normal temperature and pressure.
2. The total time for the echo to reach the hiker is the time it takes for the sound to travel to the cliff and then for the reflected sound to travel back to the hiker. This is twice the time it takes for the echo to reach the hiker.
3. Therefore, the total time it took for the echo to reach the hiker, including the to-and-fro travel, is 2 * 1.7 seconds = 3.4 seconds.
4. We can now calculate the distance the sound traveled by multiplying the speed of sound by the total time: distance = speed * time.
distance = 343 m/s * 3.4 s = 1166.2 meters.
Therefore, the estimated length of the lake is approximately 1166.2 meters.
For the person to hear the echo, the sound must travel through the length of the lake and return, make two trips through the length of the lake.
Speed of sound = 340 m/s
Distance travelled in 1.7 s = 340*1.7 m
Length of lake
= distance travelled / 2
= ?