A supersonic aircraft produces a shock wave that describes a 30° cone. What happens to the angle of the cone as the aircraft travels faster?

As the supersonic aircraft travels faster, the angle of the shock wave cone decreases. This phenomenon is known as the Mach angle effect.

To understand why this occurs, we need to consider the physics behind supersonic flow. When an aircraft flies faster than the speed of sound in air, it generates a series of shock waves around it. These shock waves are formed as a result of the pressure difference between the compressed air in front of the aircraft and the surrounding air.

The angle of the cone formed by the shock wave is directly related to the speed of the aircraft relative to the speed of sound. This relationship is described by the Mach angle equation:

sin(θ) = 1/M,

where θ is the angle of the cone and M is the Mach number of the aircraft. The Mach number is defined as the ratio of the aircraft's speed to the speed of sound.

As the aircraft's speed increases, the Mach number also increases, and therefore, the angle of the cone decreases. This means that the shock wave becomes more tightly focused, with a narrower cone angle.

In summary, as a supersonic aircraft travels faster, the angle of the shock wave cone decreases due to the relationship between the Mach number and the cone angle.