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phys: standing waves 2

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@ -659,6 +659,9 @@ For observable diffraction, the wavelength must be greater than or equal to the
A standing wave does not travel, so no energy is transferred. They are caused by the interference of symmetrical travelling waves moving in opposite directions. A standing wave does not travel, so no energy is transferred. They are caused by the interference of symmetrical travelling waves moving in opposite directions.
!!! definition
**Resonance** is when an external driver oscillating at a system's natural frequency transfers energy into the system, in this case a standing wave.
<img src="/resources/images/standing-wave.gif" width=700></img> <img src="/resources/images/standing-wave.gif" width=700></img>
The locations of zero amplitude are called **nodes** and the locations of maximum amplitude are **anti-nodes**. Adjacent nodes are separated by $\frac{\lambda}{2}$. The wave speed is determined by the medium and the wavelengths of standing waves that fit on the medium are determined by the length of the medium. The locations of zero amplitude are called **nodes** and the locations of maximum amplitude are **anti-nodes**. Adjacent nodes are separated by $\frac{\lambda}{2}$. The wave speed is determined by the medium and the wavelengths of standing waves that fit on the medium are determined by the length of the medium.
@ -671,6 +674,12 @@ $$
f_n=\frac{nv}{2L} f_n=\frac{nv}{2L}
$$ $$
Inside an **air column**, the difference in pressure allows for the formation of standing waves as waves reflect off of the interface where air changes pressure. A closed end must have nodes while open ends must have antinodes.
<img src="/resources/images/standing-tubes.png" width=700>(Source: Kognity)</img>
Resonance occurs in an air column when the length of the open tube is a multiple of half the wavelength of the sound. **Resonant lengths** occur at each antinode.
## 6.1 - Circular motion ## 6.1 - Circular motion
Circular motion is any motion along a circular path. The instantaneous velocity of an object in circular motion at any point is always tangent to its point on the circle, so the difference between any two velocities ($\Delta \vec{v}$) is radial (lies along the radius). Circular motion is any motion along a circular path. The instantaneous velocity of an object in circular motion at any point is always tangent to its point on the circle, so the difference between any two velocities ($\Delta \vec{v}$) is radial (lies along the radius).