When an aircraft flies through air, it creates pressure waves that spread outward at the speed of sound. At low speeds, these waves move ahead of the aircraft and the air has time to adjust smoothly. Near the sound barrier, the waves crowd together and pressure changes become very large.
This matters because shock waves affect aircraft design, noise, drag, and safety at high speed.
When the aircraft exceeds the speed of sound, it outruns its own pressure waves and forms a Mach cone behind it. The sharp pressure jump at the cone surface is a shock wave, and an observer hears it as a sonic boom when the cone passes by. The Mach number compares the object's speed to the local speed of sound, so Mach 1 means the object is moving exactly at sound speed.
The speed of sound depends on the air temperature, which is why high altitude conditions change the speed needed for supersonic flight.
Key Facts
- Mach number: M = v / c
- Speed of sound in air: c = sqrt(gamma R T)
- At Mach 1, v = c and pressure waves pile up near the object.
- For supersonic motion, the Mach cone angle satisfies sin(theta) = 1 / M.
- A sonic boom is caused by a rapid pressure jump when a shock wave passes an observer.
- Higher Mach number means a narrower Mach cone and stronger high-speed flow effects.
Vocabulary
- Shock wave
- A shock wave is a thin region where pressure, temperature, and density change abruptly in a fast-moving fluid.
- Sound barrier
- The sound barrier is the strong rise in aerodynamic effects that occurs as an object approaches the speed of sound.
- Mach number
- Mach number is the ratio of an object's speed to the local speed of sound.
- Mach cone
- A Mach cone is the cone-shaped boundary of pressure waves produced by an object moving faster than sound.
- Sonic boom
- A sonic boom is the loud sound heard when a shock wave from a supersonic object reaches an observer.
Common Mistakes to Avoid
- Thinking the sonic boom happens only at the instant the aircraft crosses Mach 1 is wrong because a supersonic aircraft continuously produces shock waves along its path.
- Using the speed of sound as one fixed value is wrong because it changes with temperature and therefore changes with altitude and weather conditions.
- Confusing the visible condensation cloud with the shock wave is wrong because condensation is caused by pressure and temperature changes in moist air, while the shock wave itself is a pressure discontinuity.
- Assuming a larger Mach number makes a wider cone is wrong because sin(theta) = 1 / M, so the Mach cone angle becomes smaller as speed increases.
Practice Questions
- 1 A jet flies at 680 m/s where the speed of sound is 340 m/s. What is its Mach number?
- 2 An aircraft travels at Mach 2.5. Use sin(theta) = 1 / M to find the Mach cone half-angle theta to the nearest degree.
- 3 Explain why a person on the ground can hear a sonic boom after the aircraft has already passed overhead.