<pstyle="font-size:75%;text-align: center;">Birth of the Wave Concept</p>
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#### Birth of the Wave Concept
#### Birth of Field and Wave Concepts
* Each of us has already thrown a ball, or tossed a pebble. At every moment, these
objects occupy a well-defined position in space and follow a trajectory
that our eyes can track. This sensory experience is the basis of our intuitive concept
of material bodies, well-defined objects, with limited extension in space,
and which move according to the laws of physics.
* Each of us has thrown a ball or tossed a pebble. At every moment, these objects occupy
a well-defined position in space and follow a trajectory that our eyes can track.
This sensory experience forms the basis of our intuitive concept of **material bodies**:
well-defined objects with limited spatial extent that move according to the laws of physics.
<br>
But our sensory experience is not limited to these localized objects. Each of us has
**thrown pebbles into water** or watched raindrops fall onto the calm surface of a pond.
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Their impacts disturb the water’s surface, creating **small circular ripples** that
*propagate, reinforce, or diminish* when they cross each other, and
*bend around obstacles* encountered along their path.
* These ripples manifest, *at every moment and at every point* on the surface, as a
**variation in water height** beneath the surface.
<br>
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.
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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.
<br>
* 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>
But our sensory experience is not limited to these localized objects. Each of us has already **thrown pebbles into water** or observed raindrops falling
onto the calm surface of a pond or puddle. Their impacts disturb
the surface of the water, creating **small circular ripples** that *propagate*,
*strengthen or weaken* when they cross, and *bypass obstacles*
encountered along their path.
<br>
_Animated GIF to create or purchase: rain on the pond, droplets creating ripples
that overlap and interfere._
<br>
These ripples are at the **basis of our intuitive concept of mechanical waves**,
disturbances of a continuous and extended material medium, which propagate,
can interfere, and be diffracted.
* The **properties of mechanical waves**,
**propagation*
**interference*
**diffraction* by an obstacle
**reflection and transmission* at the interface between two different material media,
**transport of energy* and momentum, *but not matter* over long
distances,
**are found in more subtle phenomena** observed in nature
and then described mathematically, or first predicted by physical theory
before being confirmed by experimentation.
* The **properties of mechanical waves**:
**Propagation*
**Interference*
**Diffraction* around an obstacle.
**Reflection and transmission* at the interface between two different media.
**Energy transport*, but *no matter transport* over long distances.
**are also found in more subtle phenomena** observed in nature and later described mathematically, or first predicted by physical theory before experimental confirmation.
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@@ -84,13 +104,13 @@ _Representation of interference and diffraction phenomena._
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#### Waves of Different Types
#### Different Types of Waves
* Today, there are **four types of waves** that have been observed, from intuitive *mechanical
waves* to *gravitational waves* and *quantum waves*, including
*electromagnetic waves*. In order, these waves **correspond to increasingly subtle
levels of reality**, related to the speed of light $`c`$,
and modeled by physical theories with increasingly abstract mathematics.
* Today, **four types of waves** have been observed, from *mechanical waves*
to *electromagnetic waves*, then *gravitational waves* and *quantum waves*.
In order, these waves **correspond to increasingly subtle levels of reality**,
linked to the speed of light *c*, and modeled by physical theories with
increasingly abstract mathematics.
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@@ -101,27 +121,32 @@ _Four types of waves in physics, to describe increasingly subtle and abstract le
##### **Mechanical Waves** *($`v \lt c`$)*
* These are therefore **the best known, most intuitive**, and they are very **easy to observe**. They correspond to a disturbance that propagates in a material medium:
**ripples* and undulations on the surface of water,
**sounds* that propagate through air,
**seismic waves* that propagate through the ground,
**oscillations* of a spring or a string of a musical instrument.
* These are the *most familiar and intuitive* and are often very
*easy to observe* or feel. They correspond to a **disturbance in a material field**:
**ripples* on the water’s surface (height field).
**sounds* propagating through air (pressure field).
**seismic waves* in the ground (displacement field in Earth).
**vibrations* in a spring or a musical instrument string (displacement field).
* All **these waves are material**, their propagation speed $`\mathscr{v}`$ is less than the speed of light $`c`$.
* All **these waves are material**; their propagation speed $`\mathscr{v}`$ is lower
than the speed of light $`c`$.
* Requiring a material medium, they *cannot travel through a vacuum*.
