Question

Shock waves have the greatest impact when the source is traveling: (A) \(\quad\) just below the speed of sound. (B) \(\quad\) exactly at the speed of sound. (C) just above the speed of sound. (D) \(\quad\) well above the speed of sound.

Short answer

B: exactly at the speed of sound.

Step-by-step solution

- Understand Shock Waves

Shock waves occur when an object travels faster than the speed of sound in a medium. They are the result of the buildup of pressure waves.

- Analyze the Speed

When an object is traveling just below the speed of sound, it compresses air in front of it, but it doesn't create shock waves. When an object travels at the speed of sound, called Mach 1, the pressure waves combine to form a strong shock wave.

- Determine the Greatest Impact

The greatest impact of shock waves occurs when the source is traveling exactly at the speed of sound because the pressure waves constructively interfere and form a single, powerful shock wave.

Key concepts

speed of sound

The speed of sound is the speed at which pressure waves travel through a medium, such as air, water, or solids. In dry air at 20°C (68°F), the speed of sound is approximately 343 meters per second (m/s) or 1235.5 kilometers per hour (km/h). This speed depends on factors like temperature, humidity, and the medium itself. Colder air slows down sound, while warmer air speeds it up.
Understanding the speed of sound is important because it serves as a benchmark for phenomena like shock waves. When an object travels at or beyond this speed, it significantly alters the way pressure waves behave around it.

pressure waves

Pressure waves are variations in pressure that travel through a medium, causing particles to compress and expand as they move. In fluids like air and water, these are longitudinal waves, meaning the particle displacement is parallel to the direction of wave propagation.
Every sound you hear is a result of pressure waves traveling through the air to your ears. In the context of shock waves, these pressure waves are created by objects moving through the medium. As an object moves, it pushes particles together, creating compressions, followed by areas of lower pressure called rarefactions.

Mach 1

Mach 1 is a term used to describe the speed of an object traveling at the speed of sound in the given medium. When an object travels at Mach 1, it is moving at the same speed as the pressure waves it generates. For instance, a jet flying at Mach 1 in air is moving at about 343 m/s.
Objects traveling at Mach 1 create significant effects due to the combination of their speed and the behavior of pressure waves. At this speed, the pressure waves generated by the object progressively merge, causing a dramatic increase in pressure known as a shock wave.

shock wave impact

Shock waves have profound impacts, particularly when an object is traveling nearly or exactly at Mach 1. These impacts are felt both environmentally and structurally. The sudden and intense buildup of pressure waves causes a sharp spike in pressure, followed by a sudden drop, resulting in what is known as a shock front.
When a shock wave hits an object, it can cause substantial damage due to the abrupt change in pressure. This is why aircraft and structures experience the greatest impact when traveling at or just beyond the speed of sound. The shock wave generated can disrupt the airflow, leading to turbulence and potential structural failure. It’s crucial to understand these effects for designing vehicles that can safely operate at such high speeds.