Serway & Jewett — Wave Motion: Problem 29

The speed of sound in air (in meters per second) depends on temperature according to the approximate expression \[ v = 331.5 + 0.607 T_C \] where \( T_C \) is the Celsius temperature. In dry air, the temperature decreases about \( 1^{\circ}\text{C} \) for every \( 150\text{-m} \) rise in altitude. (a) Assume this change is constant up to an altitude of \( 9\,000 \text{ m} \). What time interval is required for the sound from an airplane flying at \( 9\,000 \text{ m} \) to reach the ground on a day when the ground temperature is \( 30^{\circ}\text{C} \)? (b) What If? Compare your answer with the time interval required if the air were uniformly at \( 30^{\circ}\text{C} \). Which time interval is longer?