The velocity of sound in air is affected by temperature. It follows a relationship described by the formula:
v = √(γ * R * T)
Where: v is the velocity of sound, γ is the heat capacity ratio of the gas (for air, it is approximately 1.4), R is the gas constant (approximately 287 J/(kg·K)), T is the absolute temperature.
To find the corresponding velocity at 311 K, we can use the above formula. Let's calculate it:
For the initial temperature (T1) of 300 K: v1 = √(1.4 * 287 * 300)
For the final temperature (T2) of 311 K: v2 = √(1.4 * 287 * 311)
Calculating the values: v1 ≈ 341 m/s (given) v2 ≈ √(1.4 * 287 * 311) ≈ 348.7 m/s
Therefore, at 311 K, the corresponding velocity of sound would be approximately 348.7 m/s.