Update cheatsheet.en.md

10.temporary-m3p2/16.waves/20.n2/05.waves-introduction/10.waves-in-physics/cheatsheet.en.md

@@ -65,26 +65,61 @@ Physicists use the term **field** to describe a
 *physical quantity defined at every point in space and at every moment*. Here, the
 physical quantity is the water height, and the space is the two-dimensional surface
 of the pond.   
-<br>
 
-* When the *pond is calm*, its surface in **equilibrium and stable**, the *height*
-of the water beneath the surface **varies from point to point**, but this height at each point
-**does not change over time**.   
-<br>
-The physicist says the *field* of water height is **stationary**.   
 <br>
 
-* The ripples represent a variation in water height relative to
-the pond’s surface at rest. These *ripples* form the
-*basis of our intuitive concept of waves*: **disturbances in a field** that **propagate**,
-interfere, and diffract.   
-<br>
-To the physicist, a **wave** thus appears as the *non-stationary part of a field*—
-the temporary deviation from the equilibrium value of the field at rest.   
+#### Main Properties of a Field
+
+* The physicist associates the concept of a **field** with:
+   * a **physical quantity** that has *a defined value at every instant and at every point*
+     in the space where it is defined.
+   * **properties** that *specify how the field varies* in space and time,
+     and *how perturbations of the field propagate*, add together, and interact with their environment.
+
+* Let us enumerate the *main properties* of a field:
+   * A field is **uniform** if *its value is the same at every point* in space at a given
+   instant or over a specified time period.   
+   <br>
+   _*Example:* Even without ripples, the depth of a pond varies from one point to another._
+   _The water height field beneath the surface is **not uniform**._
+   _*However,* in an Olympic swimming pool where the water depth is the same everywhere,_
+   _the water height field **is uniform** at the surface._
+
+   * A field is **stationary** if *its values*—which may vary in space—*do not change over time*.
+   _*Example:* In a calm, windless pond where the water surface is "at rest," perfectly still,_
+   _the water height field is **stationary**._
+
+
+   * A field is **homogeneous** if *its propagation properties* (the shape of the perturbation 
+   for a given impact and its propagation speed in a given direction) *are identical at every point* 
+   in space, even if the field’s values vary spatially.   
+   <br>
+   _*Example:* The speed of ripples depends on depth—shallow water slows propagation due to friction_
+   _with the bottom, while deep water allows faster wave movement._
+   _*Thus,* since a pond’s depth varies, its water height field is **not strictly homogeneous**._
+   _*However,* in an Olympic pool with constant depth, the field **is homogeneous**._
+
+   * A field is **isotropic** if, regardless of the impact point, *the propagation of the perturbation*
+   (its speed, shape, and attenuation) *does not depend on direction*, even if the 
+   induced perturbation varies from one point to another for the same impact.   
+   <br>
+   _*Example:* If raindrops in a pond always create perfectly circular ripples that propagate_
+   _outward, it means each ripple spreads at the same speed in all directions._
+   _*Furthermore,* if the height of a ripple remains constant at equal distances from_
+   _the impact point, then the water height field is **isotropic**._
+
+   * A field is **linear** if, for a point-like and instantaneous impact,
+   *the amplitude of the perturbation is proportional to the energy of the impact*,
+   and if *the amplitudes of the perturbations add together simply*
+   when perturbations overlap.
+ 
 <br>
 
+#### Wave-Specific Phenomena
+
+
 * The *ripples* result from the **displacement** of water molecules—i.e., **of matter**.  
-<br>
+
 When a wave characterizes the *disturbance of a material medium*, the physicist refers to it
 as a **mechanical wave**.   
 <br>