* Circular (ripples) or spherical (sound) **waves remain centered** on the **position of the source** (duck, plane) **at the moment they were emitted**.
* Thus, the center of the circular or spherical waves moves at the speed of the source.
* Since the **speed of the wave** (ripple, sound) is **greater than that of its source** (duck, plane), part of the **wave always moves ahead of the source**, and the ripples or sound waves always surround their source.
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**The source moves through the medium at the speed of the wave**
* When a source (like a plane) moves at the same speed as the wave it produces, some of the energy it transmits to the wave accumulates at its level. The amplitude of the wave grows over time, and these vibrations act back on the source itself.
* Early aviators feared that the plane might break apart when crossing the sound barrier. The duck, however, seems unfazed as it crosses its own "ripple barrier."
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**The source moves through the medium at a speed greater than that of the wave**
* When a source (like a boat or plane) moves faster than the waves it creates, it leaves behind circular ripples (on the water's surface) or spherical waves (in the air).
* The **location where** these ripples reinforce each other forms a **V** (physicists say the ripples **interfere constructively**). This V is the **wake** left by the source.
***Inside** this V, the ripples weaken or cancel each other out, creating a **quieter zone** (physicists say the ripples **interfere destructively**).
* For a plane, this V becomes a **cone**. If you are **where the surface of this cone reaches the ground**, you hear a loud **supersonic BOOM**. Since the plane—and thus its cone—moves faster than the speed of sound, no sound can warn you in advance of this sudden BOOM.
* This BOOM is brief because **once the BOOM passes, you find yourself inside** the cone, an area of **low residual noise or silence**.
