Math Problem Statement
Calculate the air temperature (in degrees Kelvin) if the speed of sound is 353.8 m/s (at standard air pressure).
Solution
The speed of sound in air can be calculated using the following formula:
where:
- is the speed of sound,
- is the adiabatic index (ratio of specific heats, which is 1.4 for air),
- is the specific gas constant for dry air (287 J/(kg·K)),
- is the absolute temperature in Kelvin.
Rearranging the formula to solve for :
Substituting the given values:
Calculating this:
Therefore, the air temperature is approximately .
Would you like any further details or have any questions?
Here are 5 questions you might be interested in:
- How does humidity affect the speed of sound in air?
- What is the relationship between air pressure and the speed of sound?
- How can you calculate the speed of sound at different altitudes?
- What are the typical ranges for the speed of sound in various mediums?
- How does temperature inversion affect sound propagation?
Tip: When solving physics problems, always double-check unit consistency to ensure accuracy in your calculations.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Physics
Thermodynamics
Formulas
Speed of sound formula: v = sqrt(gamma * R * T)
Rearranged speed of sound formula: T = v^2 / (gamma * R)
Theorems
-
Suitable Grade Level
Advanced High School