42. A hunter wanted to know the air temperature. The echo from a nearby cliff returned 1.5 s after he fired his rifle. If the cliff is 250 m away, calculate the air temperature.

Here's how to calculate the air temperature:<br /><br />**Understanding the Concept**<br /><br />Sound travels at different speeds depending on the temperature of the air. The warmer the air, the faster sound travels. We can use the time it takes for an echo to return to calculate the speed of sound, and then use that speed to find the temperature.<br /><br />**Formula**<br /><br />The speed of sound in air (v) is related to the temperature (T in Celsius) by the following approximate formula:<br /><br />v = 331.5 + 0.6T<br /><br />**Calculations**<br /><br />1. **Calculate the speed of sound:**<br /><br />The sound travels to the cliff and back, so the total distance traveled by the sound is 2 * 250 m = 500 m. The time taken is 1.5 s. Therefore, the speed of sound (v) is:<br /><br />v = distance / time<br />v = 500 m / 1.5 s<br />v ≈ 333.33 m/s<br /><br />2. **Calculate the temperature:**<br /><br />Now we can use the speed of sound formula to find the temperature:<br /><br />333.33 m/s = 331.5 + 0.6T<br /><br />Solving for T:<br /><br />0.6T = 333.33 - 331.5<br />0.6T = 1.83<br />T = 1.83 / 0.6<br />T ≈ 3.05 °C<br /><br />**Answer**<br /><br />The air temperature is approximately 3.05 °C.<br />