1. What is the velocity of sound in air? 2. What is the distance between the two walls?
Understand the Problem
The question asks for two specific pieces of information regarding sound: the velocity of sound in air and the distance between two parallel walls based on the given scenario of echoes heard by Sunil. The first part requires understanding the physics behind sound velocity, while the second part involves calculating the distance using the time intervals provided.
Answer
The velocity of sound in air is $343 \, \text{m/s}$ and the distance between the two walls is $1689 \, \text{m}$.
Answer for screen readers
The velocity of sound in air is approximately $343 , \text{m/s}$. The distance between the two walls is approximately $1689 , \text{m}$.
Steps to Solve
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Velocity of Sound in Air The velocity of sound in air is typically around $343 , \text{m/s}$ at room temperature.
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Total Time for Echo Sunil hears the first echo after 4 seconds. The second echo is heard 2 seconds later, making the total time for the sound to travel to both walls $4 + 2 = 6 , \text{s}$.
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Calculate Distance Traveled by Sound Using the formula for distance, $d = vt$, where $v$ is the velocity of sound and $t$ is the total time, we can calculate the distance: $$ d = 343 , \text{m/s} \times 6 , \text{s} = 2058 , \text{m} $$
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Calculating Actual Distance Between Walls Since this distance includes the sound traveling to the nearest wall and coming back, we need to divide this distance by 2 to find the total distance between the two walls: $$ \text{Distance between walls} = \frac{2058 , \text{m}}{2} = 1029 , \text{m} $$
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Adding the Distance to the Nearest Wall Lastly, since the wall closest to Sunil is already at 660 m, the total distance between the walls is: $$ \text{Total Distance} = 660 , \text{m} + 1029 , \text{m} = 1689 , \text{m} $$
The velocity of sound in air is approximately $343 , \text{m/s}$. The distance between the two walls is approximately $1689 , \text{m}$.
More Information
The velocity of sound can vary based on factors such as temperature and humidity, but 343 m/s is a commonly accepted average at room temperature. The concept of echoes is used in various applications, including navigation and measurement of large distances.
Tips
Calculating the distance without considering the round trip of the sound can lead to errors. Make sure to divide the total distance by 2 to account for the sound traveling to the wall and returning.
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