The speed of sound is approximately 720 miles per hour at sea level. At this rate, how many feet does it travel in 20 seconds?
Use 1 mile = 5280 feet.
The Correct Answer and Explanation is:
To find out how many feet sound travels in 20 seconds at a speed of 720 miles per hour, we first need to convert the speed from miles per hour to feet per second.
Step 1: Convert Miles per Hour to Feet per Second
- Convert miles to feet: We know that 1 mile equals 5280 feet. Thus, to convert the speed:
[
720 \text{ miles/hour} \times 5280 \text{ feet/mile} = 3,801,600 \text{ feet/hour}
] - Convert hours to seconds: There are 3600 seconds in one hour. Therefore, to convert feet per hour to feet per second:
[
\frac{3,801,600 \text{ feet/hour}}{3600 \text{ seconds/hour}} = 1,060 \text{ feet/second}
]
Step 2: Calculate Distance Traveled in 20 Seconds
Now that we have the speed of sound in feet per second, we can find out how far it travels in 20 seconds:
[
\text{Distance} = \text{Speed} \times \text{Time}
]
Substituting the values we have:
[
\text{Distance} = 1,060 \text{ feet/second} \times 20 \text{ seconds} = 21,200 \text{ feet}
]
Conclusion
Therefore, at a speed of approximately 720 miles per hour, sound travels 21,200 feet in 20 seconds.
Explanation
Understanding how to convert units is crucial in physics and engineering. We began by converting the speed of sound from miles per hour to feet per second. This conversion is important because it allows us to work within the same measurement system (imperial units). After determining the speed in feet per second, we applied the formula for distance, which is the product of speed and time.
This approach demonstrates a fundamental principle in physics: the relationship between distance, speed, and time. Sound waves travel at a consistent speed in air, which is crucial for applications ranging from acoustics to aviation. Knowing the distance sound can travel in a given time frame helps in understanding phenomena like echoes, the delay of sound in large venues, or even in calculating distances using sound waves in sonar technology.