The speed of sound in air is about 331 m s⁻¹ at 0 °C and nearly 344 m s⁻¹ at 22 °C. Roughly how much extra time will the sound of thunder take to travel a distance of 1720 m, if the air temperature changes from 22 °C to 0 °C? Assume that all other conditions remain unchanged.
0.2 s
Explanation
To find the extra time, we calculate the time taken by sound to travel the given distance at both temperatures using the formula Time = Distance / Speed. Since the speed of sound decreases as the temperature drops from 22 °C to 0 °C, the time taken increases. The difference between the time taken at 0 °C and the time taken at 22 °C gives the extra time required.
Solution Steps
Step 1: Calculate time taken at 22 °C Using the formula, Time = Distance / Speed t₁ = 1720 m / 344 m s⁻¹ = 5 s
Step 2: Calculate time taken at 0 °C t₂ = 1720 m / 331 m s⁻¹ 5.20 s
Step 3: Calculate the extra time Extra time = t₂ - t₁ = 5.20 s - 5 s = 0.20 s (or roughly 0.2 s)