The speed of sound in air is about 343 m’s What is this speed in miles per hour?
The correct answer and explanation is :
To convert the speed of sound from meters per second (m/s) to miles per hour (mph):
Conversion:
[
\text{Speed} = 343 \, \text{m/s}
]
We use the following conversion factors:
- (1 \, \text{mile} = 1,609.34 \, \text{meters})
- (1 \, \text{hour} = 3,600 \, \text{seconds})
Now apply the conversion:
[
343 \, \text{m/s} \times \left( \frac{1 \, \text{mile}}{1,609.34 \, \text{meters}} \right) \times \left( \frac{3600 \, \text{seconds}}{1 \, \text{hour}} \right)
]
[
= 343 \times \frac{3600}{1609.34}
]
[
= 343 \times 2.23694 \approx 767 \, \text{miles per hour}
]
✅ Correct Answer: 767 miles per hour
Explanation (300+ words):
The speed of sound in air is often expressed in meters per second (m/s), which is a metric unit. However, in the United States and in certain engineering and aviation contexts, speed is commonly described in miles per hour (mph). To understand how fast sound travels in familiar terms, it’s helpful to convert between these units.
The given speed of sound is 343 meters per second, which represents how far sound can travel in one second under standard conditions (typically at 20°C or 68°F at sea level). To convert this to miles per hour, we need to change meters into miles and seconds into hours.
There are 1,609.34 meters in a mile, and 3,600 seconds in an hour. So, when converting, we multiply the speed in m/s by the number of seconds in an hour and divide by the number of meters in a mile. This gives us a unit of miles per hour (mph).
Mathematically:
[
343 \, \text{m/s} \times \frac{3600 \, \text{s/hr}}{1609.34 \, \text{miles/m}} = 767 \, \text{mph}
]
This means that under normal atmospheric conditions, sound travels at approximately 767 miles per hour. This value is important in fields like aviation, where breaking the “sound barrier” (exceeding Mach 1) refers to surpassing this speed. Supersonic aircraft and certain ballistic objects travel faster than this speed.
Understanding such conversions not only helps in grasping how fast sound actually travels, but also bridges the gap between scientific metric units and everyday imperial units.