The shock wave angle, also known as the Mach angle, is the angle formed by a shock wave produced when an object moves through a medium faster than the speed of sound.
When an object, such as an aircraft, travels at supersonic speeds (faster than the speed of sound in that medium), it outruns the sound waves it creates. Instead of radiating outwards spherically, these sound waves pile up and interfere, forming a conical shock wave that trails behind the object.
Calculating the Shock Wave Angle
The reference provided states how to find this angle:
- When a sound source moves faster than the speed of sound, a shock wave is produced as the sound waves interfere.
- The angle the shock wave produces can be found as:
sin θ = v_v / v_s = 1 / M
Let's break down the formula:
θ(theta): This is the shock wave angle itself, measured between the direction of motion of the source and the shock wave front.v_v: The velocity of the source (the object moving).v_s: The velocity of sound in the medium.M: The Mach number, which is the ratio of the source velocity to the speed of sound (M = v_v / v_s).
Essentially, the sine of the shock wave angle is equal to the reciprocal of the Mach number. As the Mach number increases (meaning the object moves much faster than sound), the sine of the angle decreases, resulting in a smaller, sharper shock wave angle.
Understanding the Mach Cone
The conical shape formed by the shock wave is often called the Mach cone. The shock wave angle θ is the half-angle of this cone. The intense sound heard as this shock wave passes an observer is known as a sonic boom.
- Lower Mach Numbers (closer to 1): Wider cone, larger
θ. - Higher Mach Numbers: Narrower cone, smaller
θ.
The shock wave angle is a critical parameter in aerodynamics and acoustics, helping to describe the nature of flow around supersonic objects and the characteristics of sonic booms.
