Calculate the air temperature (in degrees Kelvin) if the speed of sound is 353.8 m/s (at standard air pressure).

The speed of sound in air can be calculated using the following formula:

\[ v = \sqrt{\gamma \cdot R \cdot T} \]

where:
- \( v \) is the speed of sound,
- \( \gamma \) is the adiabatic index (ratio of specific heats, which is 1.4 for air),
- \( R \) is the specific gas constant for dry air (287 J/(kg·K)),
- \( T \) is the absolute temperature in Kelvin.

Rearranging the formula to solve for \( T \):

\[ T = \frac{v^2}{\gamma \cdot R} \]

Substituting the given values:

\[ v = 353.8 \, \text{m/s} \]
\[ \gamma = 1.4 \]
\[ R = 287 \, \text{J/(kg·K)} \]

\[ T = \frac{(353.8)^2}{1.4 \cdot 287} \]

Calculating this:

\[ T = \frac{125173.44}{401.8} \]

\[ T \approx 311.52 \, \text{K} \]

Therefore, the air temperature is approximately \( 311.52 \, \text{K} \).

Would you like any further details or have any questions?

Here are 5 questions you might be interested in:
1. How does humidity affect the speed of sound in air?
2. What is the relationship between air pressure and the speed of sound?
3. How can you calculate the speed of sound at different altitudes?
4. What are the typical ranges for the speed of sound in various mediums?
5. How does temperature inversion affect sound propagation?

**Tip:** When solving physics problems, always double-check unit consistency to ensure accuracy in your calculations.

Learn how to calculate air temperature (in Kelvin) from the speed of sound (353.8 m/s) using the formula v = sqrt(gamma * R * T). Detailed step-by-step solution provided, including key values for gamma (1.4), specific gas constant R (287 J/(kg·K)), and resulting temperature of approximately 311.52 K. Suitable for advanced high school students studying physics and thermodynamics.

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