The problem states that the speed of sound in air at a temperature of $x^\circ C$ is approximately $(0.6x + 331)\,\text{m/s}$. You are tasked with calculating the distance a sound travels in 5 seconds when the temperature is $10^\circ C$.

Step-by-Step Solution:

1. Determine the speed of sound at $10^\circ C$: Using the given formula: $v = 0.6x + 331$ Substitute $x = 10$: $v = 0.6(10) + 331 = 6 + 331 = 337\,\text{m/s}.$

2. Calculate the distance traveled in 5 seconds: Distance is given by: $\text{Distance} = \text{Speed} \times \text{Time}.$ Substituting the speed $v = 337\,\text{m/s}$ and time $t = 5\,\text{s}$: $\text{Distance} = 337 \times 5 = 1685\,\text{m}.$

Final Answer:

The sound travels a distance of 1685 meters in 5 seconds when the temperature is $10^\circ C$.

Would you like a detailed explanation of any step? Here are some related questions:

1. How does the speed of sound change with temperature?
2. What is the speed of sound at $0^\circ C$?
3. How long would it take for sound to travel 1 kilometer at $10^\circ C$?
4. Can this formula be applied in environments other than air (e.g., water)?
5. What happens to the speed of sound as the temperature decreases?

Tip: Always remember that the speed of sound depends on temperature due to air's changing density and elasticity!