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