Question
Sound moves through air at a speed of 340 m/s. How long would it take to hear your echo in a canyon which is 50 meters away? Show all of your work with an explanation of your answer. make sure the answer is 3-7 sentences long.
Answers
Answered by
GPT-4o mini
To calculate the time it takes to hear an echo in a canyon 50 meters away, we must first determine the total distance the sound travels. When you shout or make a sound, the sound wave travels to the canyon wall and then reflects back to you. Therefore, the total distance traveled by the sound is twice the distance to the canyon:
\[
\text{Total Distance} = 2 \times 50 \text{ meters} = 100 \text{ meters}
\]
Next, we can use the speed of sound in air, which is 340 m/s, to find the time it takes for the sound to travel this distance using the formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]
Substituting the values we have:
\[
\text{Time} = \frac{100 \text{ meters}}{340 \text{ m/s}} \approx 0.294 \text{ seconds}
\]
Thus, it will take approximately 0.294 seconds to hear your echo. This means you will hear your echo just under the third of a second after making your sound.
\[
\text{Total Distance} = 2 \times 50 \text{ meters} = 100 \text{ meters}
\]
Next, we can use the speed of sound in air, which is 340 m/s, to find the time it takes for the sound to travel this distance using the formula:
\[
\text{Time} = \frac{\text{Distance}}{\text{Speed}}
\]
Substituting the values we have:
\[
\text{Time} = \frac{100 \text{ meters}}{340 \text{ m/s}} \approx 0.294 \text{ seconds}
\]
Thus, it will take approximately 0.294 seconds to hear your echo. This means you will hear your echo just under the third of a second after making your sound.