To determine the speed of sound in air based on temperature, we can use an established formula that relates these two variables. Here, let's denote:
- [tex]\( v \)[/tex] as the speed of sound in meters per second.
- [tex]\( T \)[/tex] as the temperature in degrees Celsius.
The formula for the speed of sound in air as a function of temperature is:
[tex]\[ v = 331.3 + 0.606 \cdot T \][/tex]
Where:
- 331.3 meters per second is an approximate baseline speed of sound in dry air at 0°C.
- 0.606 meters per second per degree Celsius is the rate at which the speed of sound increases with temperature.
Now, let’s apply this equation to find the speed of sound in air at 20°C (since 68°F is approximately 20°C):
Given:
[tex]\[ T = 20 \text{°C} \][/tex]
Substituting [tex]\( T \)[/tex] into the formula:
[tex]\[ v = 331.3 + 0.606 \cdot 20 \][/tex]
Perform the multiplication:
[tex]\[ v = 331.3 + 12.12 \][/tex]
Add the results:
[tex]\[ v = 343.42 \][/tex]
Therefore, the speed of sound in air at 68°F (or 20°C) is approximately 343.42 meters per second.
