College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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#4
### Problem Statement
The speed of sound in air on a given day is 340 m/s. If a person shouts at a building and hears an echo 4 seconds later, how far away is the building?

### Explanation
When a person shouts, the sound travels to the building and the echo is the sound reflecting back to the person. The total time taken for the sound to travel to the building and back is 4 seconds.

### Step-by-Step Solution:
1. **Identify the Given Values:**
   - Speed of sound (\( v \)) = 340 m/s
   - Total time for echo (\( t \)) = 4 seconds
   
2. **Understand the Total Distance Traveled by Sound:**
   - The sound travels to the building and back, so the total distance traveled is the sum of the distance to the building and the distance back to the person.
   - Let's denote the distance to the building as \( d \). Therefore, the total distance covered by the sound \( 2d \) (to the building and back).

3. **Calculate the Distance Using the Formula:**
   - The formula to calculate distance using speed and time is: \( \text{distance} = \text{speed} \times \text{time} \).
   - From the given information, the total distance covered by the sound (\( 2d \)) is: 
     \[
     2d = v \times t
     \]
   - Substitute the given values: 
     \[
     2d = 340 \, \text{m/s} \times 4 \, \text{s}
     \]
     \[
     2d = 1360 \, \text{m}
     \]
4. **Solve for the Distance to the Building:**
   - Divide both sides of the equation by 2 to find \( d \):
     \[
     d = \frac{1360 \, \text{m}}{2}
     \]
     \[
     d = 680 \, \text{m}
     \]

### Conclusion
The building is 680 meters away from the person.
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Transcribed Image Text:### Problem Statement The speed of sound in air on a given day is 340 m/s. If a person shouts at a building and hears an echo 4 seconds later, how far away is the building? ### Explanation When a person shouts, the sound travels to the building and the echo is the sound reflecting back to the person. The total time taken for the sound to travel to the building and back is 4 seconds. ### Step-by-Step Solution: 1. **Identify the Given Values:** - Speed of sound (\( v \)) = 340 m/s - Total time for echo (\( t \)) = 4 seconds 2. **Understand the Total Distance Traveled by Sound:** - The sound travels to the building and back, so the total distance traveled is the sum of the distance to the building and the distance back to the person. - Let's denote the distance to the building as \( d \). Therefore, the total distance covered by the sound \( 2d \) (to the building and back). 3. **Calculate the Distance Using the Formula:** - The formula to calculate distance using speed and time is: \( \text{distance} = \text{speed} \times \text{time} \). - From the given information, the total distance covered by the sound (\( 2d \)) is: \[ 2d = v \times t \] - Substitute the given values: \[ 2d = 340 \, \text{m/s} \times 4 \, \text{s} \] \[ 2d = 1360 \, \text{m} \] 4. **Solve for the Distance to the Building:** - Divide both sides of the equation by 2 to find \( d \): \[ d = \frac{1360 \, \text{m}}{2} \] \[ d = 680 \, \text{m} \] ### Conclusion The building is 680 meters away from the person.
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