A airplane approaches at an altitude of 10 km flying at 600 km/hr.

1. If the air temperature at that altitude is -50 C, what is the speed of sound in air there?

2. How does that differ from the speed of sound in air typically at Earth's surface?

3. If the plane will be overhead in 1 minute, when will we hear it coming? You may assume an average speed along the path from the plane to your ear.

4. Jet engines typically emit sound over a wide spectrum of frequencies, with the maximum sound energy at 200 Hz. From this emitted sound, what frequency do you hear initially when it is 1 minute away, and what frequency do ou hear 1 minute after it has passed by?

5. What would you hear, and when would you hear it, if the plane were "hypersonic", traveling three times the speed of sound, or "Mach 3"? That's approximately the fastest military aircraft in routine service today.

To have higher speeds in air takes considerably more energy. For example, after two and half minutes of flight, when the first-stage main engines of the Space X Falcon shut down, it is 80 kilometers high and moving at Mach 10 on its way to Earth orbit. The Mach number depends on the temperature of the air.