How much time is required for a sound to travel 1 mile if the air temperature is:
0.0 Degrees Celsius
20.0 Degrees Celsius
40.0 Degrees Celsius
80.0 Degrees Celsius
Hmm, let me juggle some numbers for you! The speed of sound in dry air at 0.0 degrees Celsius is about 331.5 meters per second, or around 1079 feet per second. So, to travel 1 mile, which is roughly 5280 feet, it would take about... hmm... approximately 4.89 seconds.
Now, if we crank up the heat to 20.0 degrees Celsius, the speed of sound becomes faster, around 343.2 meters per second, or about 1126 feet per second. This means it would take a bit less time, around 4.68 seconds, to cover that mile.
At a toasty 40.0 degrees Celsius, the speed of sound increases even more, reaching approximately 355.2 meters per second, or roughly 1165 feet per second. In this case, the time taken to travel 1 mile would be approximately 4.52 seconds.
Lastly, if we venture into a scorching 80.0 degrees Celsius, the speed of sound shoots up to around 375.5 meters per second, or about 1232 feet per second. Consequently, it would take about 4.29 seconds to traverse that mile.
Of course, keep in mind that these calculations assume a constant air temperature and other factors such as humidity and wind can have an impact on the speed of sound. But hey, at least now you have a rough idea of the timescales involved. Happy travels!
To calculate the time required for sound to travel a distance, we need to use the formula:
Time = Distance / Speed.
The speed of sound in air changes with temperature. The relationship between temperature and the speed of sound in air is given by the following equation:
Speed = 331.5 + (0.6 x Temperature)
where Temperature is in degrees Celsius.
Let's calculate the time required for each temperature:
1. At 0.0 Degrees Celsius:
Using the formula, we have:
Speed = 331.5 + (0.6 x 0.0) = 331.5 m/s
Time = Distance / Speed
Time = 1 mile / (331.5 m/s)
To convert 1 mile to meters: 1 mile = 1609.34 meters
Time = 1609.34 meters / (331.5 m/s)
Time = 4.856 seconds
Therefore, it takes approximately 4.856 seconds for sound to travel 1 mile at 0.0 Degrees Celsius.
2. At 20.0 Degrees Celsius:
Using the formula, we have:
Speed = 331.5 + (0.6 x 20.0) = 343.5 m/s
Time = Distance / Speed
Time = 1 mile / (343.5 m/s)
Time = 1609.34 meters / (343.5 m/s)
Time = 4.687 seconds
Therefore, it takes approximately 4.687 seconds for sound to travel 1 mile at 20.0 Degrees Celsius.
3. At 40.0 Degrees Celsius:
Using the formula, we have:
Speed = 331.5 + (0.6 x 40.0) = 355.5 m/s
Time = Distance / Speed
Time = 1 mile / (355.5 m/s)
Time = 1609.34 meters / (355.5 m/s)
Time = 4.523 seconds
Therefore, it takes approximately 4.523 seconds for sound to travel 1 mile at 40.0 Degrees Celsius.
4. At 80.0 Degrees Celsius:
Using the formula, we have:
Speed = 331.5 + (0.6 x 80.0) = 375.5 m/s
Time = Distance / Speed
Time = 1 mile / (375.5 m/s)
Time = 1609.34 meters / (375.5 m/s)
Time = 4.285 seconds
Therefore, it takes approximately 4.285 seconds for sound to travel 1 mile at 80.0 Degrees Celsius.
Please note that these calculations assume standard atmospheric conditions and do not account for other factors like humidity or wind that can affect the speed of sound to a small extent.
What's the speed of sound in the units you want? I would convert 1 mile to ? meters. Then look up speed of sound at each temperature. Call that m/s.
m/s x #s = ?meters
Solve for #s.