To determine at which elevation sound will travel fastest, we need to understand the relationship between temperature and the speed of sound. Sound generally travels faster in warmer air because the molecules are more energetic and can transmit the sound waves more quickly.
Here's the step-by-step reasoning:
1. Given Data:
The elevations and their corresponding temperatures are given as follows:
- At 500 meters, the temperature is [tex]\(11.8^\circ C\)[/tex].
- At 1000 meters, the temperature is [tex]\(8.5^\circ C\)[/tex].
- At 1500 meters, the temperature is [tex]\(5.3^\circ C\)[/tex].
- At 2000 meters, the temperature is [tex]\(2.0^\circ C\)[/tex].
2. Understanding the Relationship:
Sound travels faster in warmer air. Thus, the elevation with the highest temperature will allow sound to travel the fastest.
3. Comparing the Temperatures:
- At 500 meters: [tex]\(11.8^\circ C\)[/tex].
- At 1000 meters: [tex]\(8.5^\circ C\)[/tex].
- At 1500 meters: [tex]\(5.3^\circ C\)[/tex].
- At 2000 meters: [tex]\(2.0^\circ C\)[/tex].
4. Identifying the Highest Temperature:
The highest temperature among the given data is [tex]\(11.8^\circ C\)[/tex], which occurs at an elevation of 500 meters.
5. Conclusion:
Therefore, sound will travel fastest at the elevation where the temperature is highest. In this case, it is at 500 meters.
So, the elevation at which sound will travel fastest is 500 meters.
