9.3 Sonic booms and shock waves

Supersonic Motion and Shock Waves

When an object moves faster than the speed of sound, it creates shock waves that pile up into what we hear as a sonic boom. Understanding how these shock waves form, how intense they get, and what factors influence them is central to acoustics at supersonic speeds.

Sonic Booms and Their Conditions

A sonic boom is the loud, explosive noise produced by shock waves when an object travels faster than the speed of sound. It's not a one-time event that happens only when the object "breaks" the sound barrier. Instead, the boom is generated continuously along the entire flight path as long as the object stays supersonic.

• Sonic booms occur when an object exceeds Mach 1 (the local speed of sound). Common examples include fighter jets like the F-16 and vehicles like the Space Shuttle during reentry.
• The pressure disturbance that reaches the ground has a characteristic N-wave signature: a sharp rise in pressure, a drop below ambient, and then a return to normal. This whole pulse typically lasts less than a second.
• A single boom can be heard across a wide strip on the ground, sometimes up to 50 miles wide, depending on altitude and atmospheric conditions.
• Temperature, air pressure, humidity, and wind all influence how the boom propagates. For instance, temperature inversions can bend shock waves toward the ground, making booms louder than expected in certain areas.

Shock Waves in Supersonic Motion

Shock waves form because the object is outrunning its own sound waves. The pressure disturbances can't propagate ahead of the object, so they pile up and compress into a thin, high-pressure front.

During supersonic travel, these compressed waves spread outward in a cone shape (called the Mach cone) trailing behind the object. The faster the object moves, the narrower the cone and the more intense the pressure jump across the shock.

There are several types of shock waves associated with a supersonic object:

• Bow shock forms at the front (nose) of the object, where air is first displaced.
• Tail shock forms at the rear, created as airflow reattaches and pressure adjusts behind the object. These two shocks are the primary sources of the "double bang" often heard during a sonic boom.
• Oblique shocks form at angled surfaces like aircraft wings and engine inlets, where the flow is deflected rather than stopped.

Mach Number and Sonic Booms

The Mach number expresses how fast an object is moving relative to the local speed of sound:

$M = \frac{v}{c}$

where $v$ is the object's velocity and $c$ is the speed of sound in the surrounding medium.

At $M = 1$, the object is at the threshold of supersonic flight and shock waves begin to form. For any $M > 1$, a sonic boom is produced continuously along the flight path. Higher Mach numbers create stronger pressure jumps across the shock, meaning louder booms on the ground.

Several factors change the effective Mach number and boom characteristics:

• Altitude: As altitude increases, air density and temperature drop, which changes the local speed of sound. An aircraft at the same indicated airspeed will have a different Mach number at different altitudes.
• Aircraft design and size: Larger aircraft generally produce stronger booms. Designs like the Concorde produced significant booms, while NASA's X-59 QueSST is specifically shaped to reduce boom intensity at ground level.
• Atmospheric conditions: Temperature inversions and wind shear can refract shock waves, focusing or dispersing the boom energy before it reaches the surface.

Impacts and Mitigation of Sonic Booms

Environmental impacts:

• Wildlife disturbance is a real concern. Marine mammals can be startled by underwater-transmitted booms, and nesting birds may abandon nests in response to repeated exposure.
• Structural damage is possible, though usually minor: cracked windows, loosened plaster, and in extreme cases, weakened building elements from repeated exposure.
• Sonic booms contribute to overall noise pollution, particularly near military training routes.

Societal impacts:

• Populations under supersonic flight paths experience sleep disturbance, heightened stress, and general annoyance. These effects were a major reason supersonic commercial flight never expanded beyond a few routes.
• Most countries ban overland supersonic flight over populated areas, which severely limited the Concorde's route options and increased operating costs.

Mitigation strategies:

1. Route supersonic flight paths over oceans or unpopulated areas.
2. Establish high-altitude supersonic corridors where booms attenuate before reaching the ground.
3. Modify aircraft shape using low-boom design principles (elongated nose, carefully sculpted fuselage) to spread the pressure signature and reduce peak overpressure.
4. Use operational techniques such as accelerating only at higher altitudes and employing the Mach cutoff technique, where the aircraft flies just fast enough that atmospheric refraction bends the shock waves upward before they reach the surface.

Regulatory approaches:

• Overland supersonic flight bans remain in effect in most jurisdictions.
• International bodies like ICAO are developing noise standards specifically for future supersonic aircraft.
• As low-boom designs mature, regulations may evolve to permit supersonic overland flight below certain noise thresholds.