Question

Hiking in the mountains, you shout "hey," wait \(2.00 \mathrm{~s}\) and shout again. What is the distance between the sound waves you cause? If you hear the first echo after \(5.00 \mathrm{~s}\), what is the distance between you and the point where your voice hit a mountain?

Short answer

Answer: The distance between the person and the point where their voice hits the mountain is 857.5 meters.

Step-by-step solution

Find the speed of sound in air

The typical speed of sound in air at room temperature (20 degrees Celsius) is approximately 343 meters per second (m/s). We'll use this speed in our calculations.

Calculate the distance between the sound waves

To find the distance between the two sound waves caused by the shouts, we can use the formula distance = speed * time. We know the time between the shouts is 2 seconds, and we already know the speed of sound in air. Therefore, we can calculate the distance like this: Distance = 343 m/s * 2 s Distance = 686 meters So, the distance between the two sound waves is 686 meters.

Calculate the round-trip time for the echo

The problem states that the first echo is heard after 5 seconds. This means that the sound has traveled to the mountain and then back to the person. To find the time it takes for the sound to reach the mountain, we need to divide the total time by 2: Time to reach the mountain = 5 s / 2 = 2.5 s

Calculate the distance between the person and the mountain

Now that we know the time it takes for the sound to travel to the mountain, we can use the same formula, distance = speed * time, to find the distance between the person and the mountain: Distance = 343 m/s * 2.5 s Distance = 857.5 meters So, the distance between the person and the mountain is 857.5 meters.